A065018 a(n) = Sum_{d|n} sigma(d)^2.
1, 10, 17, 59, 37, 170, 65, 284, 186, 370, 145, 1003, 197, 650, 629, 1245, 325, 1860, 401, 2183, 1105, 1450, 577, 4828, 998, 1970, 1786, 3835, 901, 6290, 1025, 5214, 2465, 3250, 2405, 10974, 1445, 4010, 3349, 10508, 1765, 11050, 1937, 8555, 6882
Offset: 1
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
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PARI
{ for (n=1, 1000, a=sumdiv(n, d, sigma(d)^2); write("b065018.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 03 2009 -
PARI
my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^2*x^k/(1-x^k))) \\ Seiichi Manyama, May 08 2021
Formula
Dirichlet convolution of A072861 and A000012. Dirichlet g.f.: zeta^2(s)*zeta^2(s-1)*zeta(s-2)/zeta(2s-2). - R. J. Mathar, Feb 03 2011
Sum_{k=1..n} a(k) ~ 5 * Zeta(3)^2 * n^3 / 6. - Vaclav Kotesovec, Feb 01 2019
From Seiichi Manyama, May 08 2021: (Start)
G.f.: Sum_{k >= 1} sigma(k)^2 * x^k/(1 - x^k).
If p is prime, a(p) = 1 + (p+1)^2. (End)