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URL: https://oeis.org/A386745

⇱ A386745 - OEIS

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A386745
a(n) = n^2*sigma_2(n).
5
0, 1, 20, 90, 336, 650, 1800, 2450, 5440, 7371, 13000, 14762, 30240, 28730, 49000, 58500, 87296, 83810, 147420, 130682, 218400, 220500, 295240, 280370, 489600, 406875, 574600, 597780, 823200, 708122, 1170000, 924482, 1397760, 1328580, 1676200, 1592500, 2476656
OFFSET
0,3
LINKS
FORMULA
G.f.: Sum_{k>=1} k^4*x^k*(1 + x^k)/(1 - x^k)^3. - Amiram Eldar, Aug 01 2025
a(n) = n^2*A001157(n).
Dirichlet g.f.: zeta(s-2)*zeta(s-4). - R. J. Mathar, Aug 03 2025
Sum_{k=0..n} a(k) ~ zeta(3) * n^5 / 5. - Amiram Eldar, Nov 11 2025
MATHEMATICA
Table[n^2*DivisorSigma[2, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + x^k)/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]
PROG
(PARI) a(n) = if (n, n^2*sigma(n, 2), 0); \\ Michel Marcus, Aug 01 2025
(Magma) [0] cat [n^2*DivisorSigma(2, n): n in [1..45]]; // Vincenzo Librandi, Aug 04 2025
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Vaclav Kotesovec, Aug 01 2025
STATUS
approved