A333808 - OEIS

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A333808

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

0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 10, 0, 2, 3, 2, 5, 5, 0, 2, 3, 7, 0, 5, 0, 2, 8, 2, 0, 5, 0, 7, 3, 2, 0, 5, 5, 9, 3, 2, 0, 10, 0, 2, 10, 2, 5, 5, 0, 2, 3, 14, 0, 5, 0, 2, 8, 2, 7, 5, 0, 7, 3, 2, 0, 12, 5, 2, 3, 2, 0, 10

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..90.

FORMULA

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

MATHEMATICA

Table[DivisorSum[n, # &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 90}]

nmax = 90; CoefficientList[Series[Sum[Prime[k] x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A008472, A070039, A097974, A333806, A333807.