A339353 G.f.: Sum_{k>=1} k^2 * x^(k*(k + 1)) / (1 - x^k).

0, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 14, 1, 5, 10, 5, 1, 14, 1, 21, 10, 5, 1, 30, 1, 5, 10, 21, 1, 39, 1, 21, 10, 5, 26, 30, 1, 5, 10, 46, 1, 50, 1, 21, 35, 5, 1, 66, 1, 30, 10, 21, 1, 50, 26, 70, 10, 5, 1, 91, 1, 5, 59, 21, 26, 50, 1, 21, 10, 79, 1, 130, 1, 5, 35, 21, 50, 50, 1, 110

Offset: 1

Author

Ilya Gutkovskiy, Dec 01 2020

Keywords

• nonn

Comments

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

Links

• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A001157, A056924, A067558, A070039, A095118, A339354.

Programs

Mathematica

nmax = 80; CoefficientList[Series[Sum[k^2 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, #^2 &, # < Sqrt[n] &], {n, 80}]

PARI

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