A379813 a(n) = sigma_1(n) * sigma_3(n).

1, 27, 112, 511, 756, 3024, 2752, 8775, 9841, 20412, 15984, 57232, 30772, 74304, 84672, 145111, 88452, 265707, 137200, 386316, 308224, 431568, 292032, 982800, 488281, 830844, 817600, 1406272, 731700, 2286144, 953344, 2359287, 1790208, 2388204, 2080512, 5028751

Offset

1,2

Comments

See A379812 for more links and Ramanujan's general formula.

References

Srinivasa Ramanujan, Collected papers, edited by G. H. Hardy et al., Chelsea, 1962, chapter 17, pp. 133-135.

Links

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

Srinivasa Ramanujan, Some formulae in the analytic theory of numbers, Messenger of Mathematics, Vol. 45 (1916), pp. 81-84.

Formula

a(n) = A000203(n) * A001158(n).

Multiplicative with a(p^e) = (p^(e+1)-1) * (p^(3*e+3)-1) / ((p-1) * (p^3-1)).

Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(s-3) * zeta(s-4) / zeta(2*s-4).

Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = 7 * zeta(5) / 4 = 1.81462357150089737107... .

Mathematica

a[n_] := Times @@ DivisorSigma[{1, 3}, n]; Array[a, 50]

Prog

(PARI) a(n) = {my(f = factor(n)); sigma(f) * sigma(f, 3); }

Crossrefs

Cf. A000203, A001158, A013663, A072861, A091258, A091259, A092348, A092345, A356533, A356534, A379812, A379814.

Sequence in context: A143938 A042428 A158554 * A267812 A029699 A087795

Adjacent sequences: A379810 A379811 A379812 * A379814 A379815 A379816

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 03 2025

Status

approved