A347142 Sum of 4th powers of divisors of n that are < sqrt(n).

0, 1, 1, 1, 1, 17, 1, 17, 1, 17, 1, 98, 1, 17, 82, 17, 1, 98, 1, 273, 82, 17, 1, 354, 1, 17, 82, 273, 1, 723, 1, 273, 82, 17, 626, 354, 1, 17, 82, 898, 1, 1394, 1, 273, 707, 17, 1, 1650, 1, 642, 82, 273, 1, 1394, 626, 2674, 82, 17, 1, 2275, 1, 17, 2483, 273, 626

Offset

1,6

Links

Table of n, a(n) for n=1..65.

Formula

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

Mathematica

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

Prog

(PARI) A347142(n) = { my(s=0); fordiv(n, d, if((d^2)>=n, return(s)); s += (d^4)); }; \\ Antti Karttunen, Aug 19 2021

Crossrefs

Cf. A001159, A056924, A070039, A279363, A339353, A339354, A347143.

Sequence in context: A229201 A040303 A040304 * A347143 A378472 A124517

Adjacent sequences: A347139 A347140 A347141 * A347143 A347144 A347145

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 19 2021

Status

approved