A333750 - OEIS

A333750

Number of prime power divisors of n that are <= sqrt(n).

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 3, 0, 1, 1, 3, 0, 2, 0, 2, 2, 1, 0, 3, 1, 2, 1, 2, 0, 2, 1, 3, 1, 1, 0, 4, 0, 1, 2, 3, 1, 2, 0, 2, 1, 3, 0, 4, 0, 1, 2, 2, 1, 2, 0, 4, 2, 1, 0, 4, 1, 1, 1, 3, 0, 4, 1, 2, 1, 1, 1, 4, 0, 2, 2, 3

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OFFSET

1,12

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

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

MAPLE

f:= proc(n) local p;

add(min(padic:-ordp(n, p), floor(1/2*log[p](n))), p=numtheory:-factorset(n))

end proc:

map(f, [$1..200]); # Robert Israel, Apr 22 2020