A379814 a(n) = sigma_2(n) * sigma_3(n).

1, 45, 280, 1533, 3276, 12600, 17200, 49725, 68887, 147420, 162504, 429240, 373660, 774000, 917280, 1596221, 1425060, 3099915, 2483320, 5022108, 4816000, 7312680, 6449040, 13923000, 10253901, 16814700, 16760800, 26367600, 20536380, 41277600, 28659904, 51117885

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) = A001157(n) * A001158(n).

Multiplicative with a(p^e) = (p^(2*e+2)-1) * (p^(3*e+3)-1) / ((p^2-1) * (p^3-1)).

Dirichlet g.f.: zeta(s) * zeta(s-2) * zeta(s-3) * zeta(s-5) / zeta(2*s-5).

Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(3) * zeta(4) * zeta(6) / zeta(7) = Pi^10 * zeta(3) / (85050 * zeta(7)) = 1.31261826893951336264... .

Mathematica

a[n_] := Times @@ DivisorSigma[{2, 3}, n]; Array[a, 50]

Prog

(PARI) a(n) = {my(f = factor(n)); sigma(f, 2) * sigma(f, 3); }

Crossrefs

Cf. A001157, A001158, A091260, A092344, A092344, A298754, A379812, A379813.

Cf. A002117, A013662, A013664, A013665.

Sequence in context: A178540 A351534 A296326 * A064561 A291177 A341568

Adjacent sequences: A379811 A379812 A379813 * A379815 A379816 A379817

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 03 2025

Status

approved