Problem 51975. Compute a sum of Ramanujan

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 160.675px 7.79167px; transform-origin: 160.675px 7.79167px; unicode-bidi: normal; "><span style="">Srinivasa Ramanujan defined the following function:</span></span></div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUUAAABaCAYAAAAvg0SnAAALrUlEQVR4nO2dzZGruhaFVw7OwAk4AQ/u2BE4A2fQGTiFjsEhOIeO4FY5gjfoFO4b4FVsqyUhQBIC1lelOtWmaTgYFlv7T4AQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIUQGzu8hhBC75gbgF8B/7/GDT3E8vz/7D8ALwBeAQ+VzFEKIKlzQid0JndB9v3/+BXB8f86fn+jF8xsSRiHEBnmhsxQtD3TC93xvf5htB/RWo6baQohNcUQnbhfn8wM6MaQwutC6/Cp6dkIIUZkzOnG7erZR+F7wT5P/A3Avd2pCCFEf+gsf+Ct8N/SBF5/4hcRUCCFWDafJN3TCeEA3Leb0+NdsJ9f350IIsTk4TXYHRfBqPvtGZzX+orMyhRBik5zRCd7z/a8bVT45249Vz04IIYQQQgghhBBCCCH2wQF/q4WEEGJ3MK3pF0pdEmJRmF/YytijILgdh/Z4DYRoBl/O4S86scw57ujSc56e47ljT1UvN3TpTLZ2XKIoxMKw9ZcdpRs3nNCJH7vr2PFT+NitwheGRFGIhbGtveyo1ebL+tNqH7slJIpCNAQbPbjT6JpNYQ/oLcfvisdtBYmiEI1hu9xwPKJ7lD2PvZUGShSFaBCfj2+JvLk79teQVqIoRIPYKKgdS3S42VvARaIoRKOwu7YdoW7apc9jT1NoiWJhTugucq4b+fj+e+qJtw98Sd17DH7URKI4ABNdp/hzcgsi4dRqi8K41v/TAf2C9LmtKl+i9Z4Sq2sjUYxgqwzG3oQndMJVatrBv7+V9XvP6NcmXhN88fmmubly/I74zB3kA7unKW1NJIoR7uhvwjHiwyTc0tHCL/iXsVwTrqis6UYMLQdgh7sEac5j7S0AUguJYgRWF4y9+b7QWQo18C2IvhZu6K7VBb0ltJYb8YDuXJ/4tAgv+Gs55rLm7UuaQ0uV5keiGICLjY+tP+XDUsvnw84ea59Gl74RGcnN9ffv6F6WoetuhTHXSytUBpjLGhUdEsUAdiW0Mb4h1o7W4oBtON7XJopDq+LZ6W7OapQT/P7Ftb8UW0KiGIAVBWMvzAv1S7KeWL9/aU2ieERaWkypEj37wuZYu2+5JWiNSxTR3exnfHYKeb1/PmM4XYTF/HOmSyf0fd3IUJoHc9nWbC2sSRRTKdn+y1cGuLdyvNwc8Tcv9Avrfq4mc0R/kz3wWZDPQADfHneELxL3G5uKYVs2PdBHla1jPWWqNiUFhC+CuWPujbM1UbQ+6RK5l6EywD22+soBjaHQ2JXf9oreKuTNa98WtNDsTR6K+N2dfVJgvqH78NBXmPIg84GfYinkaoM/98HfmihyiltyWutrM7al3FWxAKFgCq1CN63mifiNx+2pWKe5T1R4bkP+Kwr2FFG8oq/amTPmJhJvTRT5/yldoeN7qS3RZkxsAFslYMXEWmiuRWjTLOaKohVEX+TYnkdKZHntzvYcohib3tO18TvwezlEbI7lPgU3L1K10WISoYcwlopjUyFifzOFocRwm9KRMh2SKOZxA8y1sujrqylMzI2N3U9CRLEtmdxIsV08yGJ9iiHxSRVFK7whBy7PI/UmX/u0KYcoxqb3Nuk59ntzrbsHyjQBiUHfYiyZXIgoNp3B9YUx6OEKnxuR9pEqijxGqBQwJahj4UMx5YFW9Dkf36gviHQDDSWTCxHFRuosNprnWpA2/SF009PpHQs62GOEBM9aqykpFnzgp+RHKvqchyUE0Zb9KRVHTMZOnV2/j7UGT4F9YtYYp8WxG9Qewzd1drstpzxkKceN7avo8zy4wHzsu8phTbvwmi1d4vkvgP9pND/+CXx/H6ITii67FmRqt5yU1BhrmbmiyIg0p/c83hVxK5D5kWtmraJ4xXDfzBPyB0A4m2ihS45EcR3jn8D3B8BvKR4Cn9OyS02K/UE84HGBX5TP6P1CL7OdD13s2EvUW+dmjaJIC51VSL5xfx8zZ3oO70ml3ohs0LKyb3grVpyO2JsvderDfYZEjMf6eQ/rKOe2XwwLIq1T1+pcE67LoIR/LLco+poyhEbOLtk8riLNIjusL/5F7yS3Fhxrj8fezMwZi013D+YYD/z1Cd3QrwszdOPfUa+hbW7O6K+9O+7IK/S5u+SM8bfmmuLSvaJSvrqwScvuovuhVJwp3FDnxqUAK/I4DDugrLWTjFJv6mNdWdZg2sULyabJ5HpociQCD/GA/Ep7YOnUm6HWdVvE7aB/RP8dLB3tr0IoFWcOvJFL3cRXyK+0F5iNsMTDyPt4Dle08fK+oLuWKc+Mr10Y4w4tRPyLUyryyZXqck93Sq0nLdqDqTdLico35olAaUHkets3pAneGdONCfqlWwxq2gbZWa53KJk7Bwekv51SYCt8CeL2sSk/S8Cc2qkvdc5mSnBA9xzYmvbUY7FgYSzfaC/17YTunKzvc7Yle0F3MZ9QwEK0A6dqS7hI+CIfIzQujJSXDgqN7RNAxvr82Rm/RSsRSGsyI8RqoaDUXqWPEXrbIm/qekNP1Jny2xzXMUYNxTRl3aVvfF6TFkXHVsoJsSkY9axhZdEfx5xdX+L5HN9bjYj1HDFgm7cUOF2fYz2XhN/fmnuqCvEHm3rD6V2u4SaUp1TiTPWfsSihBnPEgC6KMeLN47Xm08+dUihEE/iWLV1yTJkmclo6Z5nfMcwVg7G+yBaXE57qQhCiaWyubAtjanoa/x9zpv5sXEw4zXeFyPYrmCoG7MqeytfI358KU2ysFXuC/7rapZCFEI1Ba3csTDWj5Ubx4Wc+kb57tl3xaXF/IS7QobZ7B/in1S+UtYLZFesH3bk/0HdaClngdLlYl8WX+ZyVOXurShKiCX4wvkHJFf5GF9YS9PkofWIAdIIw1OPS/q7P0qTvkE1hGGgpFVE/mGO6wmdzMV2Bty0P3f3o221pqi/Eajghz8MzNujB/DpfAxXrK3NLHENiQEtx7PFdUTyjj04z6FXK0rIBNp8lGGp+DXy+OKxgfgf+lhCrh41qS+X9sQ1aruDBGFG0Ccc+wblEttt9KQY3jA+41F6j28UKYuj7jW133Qu0aBVwEZuGfq/cDSHu+HTS1xRFtkKLRX95br7AhhUDCsEUYVtaFIeuv7WIfdkALO97oO/kI0EUm4eWXKnp2xKiaFesDB3XLssR2vZAfOo5xJyVMGnBTxmcjvMahF4M1iJ2r5O7P18y6rcpNk/IWsr592uKon2YQ1PGWC2v7X9KazHklxyCKURTrKtQ1/iUwe5BMfcB0Iu/7/u3aVy2DLG1phVCZIWWTMkefjlF8Ynh6PPQMr/AZ9eX2P5nfE5Bxyacz+0ENAcKWeiFZ18Mvuk9U4/oQrApOEq/EZuFD+0F3Y1v1+85ol8/JHX4HpacokjrJ4bNI/Qd09Yz+wSD+1N8reU5ttwv5XxLYK1d3wuPNfAxsed2WttDIirEJuDbn+LxwOcDklrHHHu4copiKMXFYs/ZPSZ7MLr+xLv5m64YAJ9CS6vvgOGIPdsG1ia2/jytPvflwY49wKeo2gCcz5XAJrxCrB5GHtlT0QpDTnKKIs859hCGprtc8O3kbLfNXc+Bfe3n7ErvWynTUrtO22KjyraLPiPIN3x25XH7U1pr2n5v9nMuspWayC5E8zBPjxHWUqkWOUUR6M83hJ3uUhRY2sY6ZxtAcMvXQudrxfaF4YADrdqlKj5soOWF3oKmkFuL2m0lx22+62wrYEqXJQpRFVvbG/I9teZTBHpRiwUvOBVkUror+LQOXUvPrsnug23SUnxqrK1eEvqI6Se238EZ4fXnbRTbhW6DJ9psiCvEZF7oI4k2ymhpzadIHmg7NeSM+p3NhRAzoBAyCMCpFi2gnNUtJUSR0dMWqyvoZ9vF+s1CbAX6uyiC1lr8Qr4H2vr3cjvjT5iWUF2akt1uhBCFoK/J+uUuCPuRpsDILv1TJaLbPOdWhLH0OtRCCDGIza9bkguU1CyEEEIIIYQQQgghhBBCCCGEEEJk4v/WSOigWbq8pQAAAABJRU5ErkJggg==" alt="phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]" style="width: 162.5px; height: 45px;" width="162.5" height="45"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.9917px 7.79167px; transform-origin: 86.9917px 7.79167px; unicode-bidi: normal; "><span style="">Write a function to compute </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="phi(a)" style="width: 32.5px; height: 18.5px;" width="32.5" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 66.5083px 7.79167px; transform-origin: 66.5083px 7.79167px; unicode-bidi: normal; "><span style=""> for various values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.85px 7.79167px; transform-origin: 82.85px 7.79167px; unicode-bidi: normal; "><span style="">. See also Cody Problems </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45960"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">45960</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "><span style=""> and </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">46000</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Problem 51975. Compute a sum of Ramanujan

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Problem 51975. Compute a sum of Ramanujan

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Last 200 Solutions

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