A326121 - OEIS

A326121

Expansion of Sum_{k>=1} k^2 * x^(2*k) / (1 - k * x^k).

0, 1, 1, 5, 1, 18, 1, 33, 28, 58, 1, 246, 1, 178, 369, 577, 1, 1539, 1, 2774, 2531, 2170, 1, 16706, 3126, 8362, 20413, 35366, 1, 116444, 1, 135425, 178479, 131362, 94933, 1110999, 1, 524650, 1596521, 2530946, 1, 7280892, 1, 8403734, 16364457, 8389138, 1, 78568322, 823544, 43420683

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(n) = Sum_{d|n, d>1} (n/d)^d = Sum_{d|n, d<n} d^(n/d).

a(p) = 1, where p is prime.

a(n) = A055225(n) - n.

MATHEMATICA

nmax = 50; CoefficientList[Series[Sum[k^2 x^(2 k)/(1 - k x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Table[DivisorSum[n, (n/#)^# &, # > 1 &], {n, 1, 50}]