A347143 Sum of 4th powers of divisors of n that are <= sqrt(n).

1, 1, 1, 17, 1, 17, 1, 17, 82, 17, 1, 98, 1, 17, 82, 273, 1, 98, 1, 273, 82, 17, 1, 354, 626, 17, 82, 273, 1, 723, 1, 273, 82, 17, 626, 1650, 1, 17, 82, 898, 1, 1394, 1, 273, 707, 17, 1, 1650, 2402, 642, 82, 273, 1, 1394, 626, 2674, 82, 17, 1, 2275, 1, 17, 2483, 4369, 626

Offset: 1

Author

Ilya Gutkovskiy, Aug 19 2021

Keywords

• nonn

Crossrefs

Cf. A001159, A038548, A066839, A095118, A279363, A280375, A347142.

Programs

Mathematica

Table[DivisorSum[n, #^4 &, # <= Sqrt[n] &], {n, 1, 65}]
nmax = 65; CoefficientList[Series[Sum[k^4 x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PARI

A347143(n) = { my(s=0); fordiv(n,d,if((d^2)>n,return(s)); s += (d^4)); (s); }; \\ Antti Karttunen, Aug 19 2021

Formula

G.f.: Sum_{k>=1} k^4 * x^(k^2) / (1 - x^k).