A321295 a(n) = n * sigma_n(n).

1, 10, 84, 1092, 15630, 284700, 5764808, 134744072, 3486961557, 100097666500, 3138428376732, 107019534520152, 3937376385699302, 155577590681061500, 6568408813691796120, 295152408847700721680, 14063084452067724991026, 708238048886859220660710

Offset: 1

Author

Ilya Gutkovskiy, Nov 02 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..385

Crossrefs

Cf. A023887, A064987.

Programs

Magma

[n*DivisorSigma(n, n): n in [1..20]]; // Vincenzo Librandi, Nov 06 2018

Mathematica

Table[n DivisorSigma[n, n], {n, 18}]
nmax = 18; Rest[CoefficientList[Series[Sum[k^(k + 1) x^k/(1 - (k x)^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Sum[EulerPhi[n/d] DivisorSigma[n + 1, d], {d, Divisors[n]}], {n, 18}]

PARI

a(n) = n*sigma(n, n); \\ Michel Marcus, Nov 03 2018

Perl

use ntheory ":all"; say "$ ",vecprod($,divisor_sum($,$)) for 1..30; # Dana Jacobsen, Nov 05 2018

Formula

G.f.: Sum_{k>=1} k^(k+1)*x^k/(1 - (k*x)^k)^2.

a(n) = Sum_{d|n} phi(n/d)*sigma_(n+1)(d).

a(n) = n * A023887(n).