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A002604
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a(n) = n^6 + 1.
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6
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1, 2, 65, 730, 4097, 15626, 46657, 117650, 262145, 531442, 1000001, 1771562, 2985985, 4826810, 7529537, 11390626, 16777217, 24137570, 34012225, 47045882, 64000001, 85766122, 113379905, 148035890
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OFFSET
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0,2
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COMMENTS
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Because of Fermat's little theorem, a(n) is never divisible by 7. - Altug Alkan, Apr 08 2016
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LINKS
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FORMULA
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G.f. (-1 + 5*x - 72*x^2 - 282*x^3 - 317*x^4 - 51*x^5 - 2*x^6) / (x - 1)^7. - R. J. Mathar, Aug 06 2012
Sum_{n>=0} 1/a(n) = 1/2 + Pi * (coth(Pi) + (sinh(Pi) + sqrt(3)*sin(sqrt(3)*Pi)) / (cosh(Pi) - cos(sqrt(3)*Pi))) / 6 = 1.5171007340332164261529... . - Vaclav Kotesovec, Feb 14 2015
Sum_{n>=0} (-1)^n/a(n) = 1/2 + Pi/(6*sinh(Pi)) + Pi * (sqrt(3)*cosh(Pi/2) * sin((sqrt(3)*Pi)/2) + cos((sqrt(3)*Pi)/2) * sinh(Pi/2)) / (3*(cosh(Pi) - cos(sqrt(3)*Pi))) = 0.514210347292695053493... . - Vaclav Kotesovec, Feb 14 2015
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MATHEMATICA
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LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 2, 65, 730, 4097, 15626, 46657}, 30] (* Harvey P. Dale, Jul 28 2021 *)
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PROG
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(PARI) a(n)=n^6+1
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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