A339354 G.f.: Sum_{k>=1} k^3 * x^(k*(k + 1)) / (1 - x^k).

0, 1, 1, 1, 1, 9, 1, 9, 1, 9, 1, 36, 1, 9, 28, 9, 1, 36, 1, 73, 28, 9, 1, 100, 1, 9, 28, 73, 1, 161, 1, 73, 28, 9, 126, 100, 1, 9, 28, 198, 1, 252, 1, 73, 153, 9, 1, 316, 1, 134, 28, 73, 1, 252, 126, 416, 28, 9, 1, 441, 1, 9, 371, 73, 126, 252, 1, 73, 28, 477, 1, 828, 1, 9, 153, 73, 344

Offset: 1

Author

Ilya Gutkovskiy, Dec 01 2020

Keywords

• nonn

Comments

Sum of cubes of divisors of n that are smaller than sqrt(n).

Links

• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A001158, A056924, A070039, A276634, A280375, A339353.

Programs

Mathematica

nmax = 77; CoefficientList[Series[Sum[k^3 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, #^3 &, # < Sqrt[n] &], {n, 77}]

PARI

a(n) = sumdiv(n, d, if (d^2 < n, d^3)); \\ Michel Marcus, Dec 02 2020