A321259 a(n) = sigma_n(n) - n^n.

0, 1, 1, 17, 1, 794, 1, 65793, 19684, 9766650, 1, 2194095090, 1, 678223089234, 30531927033, 281479271743489, 1, 150196195641350171, 1, 100000096466944316978, 558545874543637211, 81402749386839765307626, 1, 79501574308536809523296482, 298023223876953126

Offset: 1

Author

Ilya Gutkovskiy, Nov 01 2018

Keywords

• nonn

Comments

a(n) is the sum of n-th powers of proper divisors of n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..400
• Eric Weisstein's World of Mathematics, Proper divisors
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000312, A001065, A023887, A067558, A276634, A279363, A279364, A292919, A321258.

Programs

Magma

[DivisorSigma(n, n) - n^n: n in [1..30]]; // Vincenzo Librandi, Nov 02 2018

Mathematica

Table[DivisorSigma[n, n] - n^n, {n, 25}]
nmax = 25; Rest[CoefficientList[Series[Sum[(k x)^(2 k)/(1 - (k x)^k), {k, 1, nmax}], {x, 0, nmax}], x]]

PARI

a(n) = sigma(n, n) - n^n; \\ Michel Marcus, Nov 02 2018

Formula

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

a(n) = A023887(n) - A000312(n).

a(n) = A321258(n,n).

a(n) = 1 if n is prime.