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
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.
Crossrefs
Programs
-
Mathematica
a[n_] := Times @@ DivisorSigma[{2, 3}, n]; Array[a, 50] -
PARI
a(n) = {my(f = factor(n)); sigma(f, 2) * sigma(f, 3);}
Formula
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... .
Comments