Voozh

A347158

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

0, 0, 0, 0, 0, 16, 0, 16, 0, 16, 0, 97, 0, 16, 81, 16, 0, 97, 0, 16, 81, 16, 0, 97, 0, 16, 81, 16, 0, 722, 0, 16, 81, 16, 625, 97, 0, 16, 81, 641, 0, 97, 0, 16, 706, 16, 0, 97, 0, 641, 81, 16, 0, 97, 625, 2417, 81, 16, 0, 722, 0, 16, 2482, 16, 625, 97, 0, 16, 81, 3042

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

Table of n, a(n) for n=1..70.

FORMULA

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

MATHEMATICA

Table[DivisorSum[n, #^4 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 70}]

nmax = 70; CoefficientList[Series[Sum[Prime[k]^4 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A001159, A005065, A005068, A333806, A333808, A347142, A347156, A347157.