A356533 a(n) = sigma_2(n)^2.

1, 25, 100, 441, 676, 2500, 2500, 7225, 8281, 16900, 14884, 44100, 28900, 62500, 67600, 116281, 84100, 207025, 131044, 298116, 250000, 372100, 280900, 722500, 423801, 722500, 672400, 1102500, 708964, 1690000, 925444, 1863225, 1488400, 2102500, 1690000, 3651921

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (15), a=b=2.

Formula

Dirichlet g.f.: zeta(s) * zeta(s-2)^2 * zeta(s-4) / zeta(2*s-4).

Multiplicative with a(p^e) = ((p^(2*e+2)-1)/(p^2-1))^2. - Amiram Eldar, Aug 11 2022

a(n) = A001157(n)^2. - R. J. Mathar, Aug 18 2022

Mathematica

Table[DivisorSigma[2, n]^2, {n, 1, 40}]

Prog

(PARI) a(n) = sigma(n, 2)^2; \\ Michel Marcus, Aug 11 2022

Crossrefs

Cf. A001157, A127473, A035116, A072861, A356535 (partial sums).

Sequence in context: A134422 A016850 A309779 * A221274 A042220 A114254

Adjacent sequences: A356530 A356531 A356532 * A356534 A356535 A356536

Keyword

nonn,mult

Author

Vaclav Kotesovec, Aug 11 2022

Status

approved