A364419 - OEIS

A364419

Number of divisors of n of the form 5*k+3 that are at most sqrt(n).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1

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OFFSET

1,72

LINKS

Table of n, a(n) for n=1..99.

FORMULA

G.f.: Sum_{k>=0} x^(5*k+3)^2 / (1 - x^(5*k+3)).

MATHEMATICA

Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{3}, Mod[#, 5]] &)], {n, 99}]

nmax = 99; CoefficientList[Series[Sum[x^(5 k + 3)^2/(1 - x^(5 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A001878, A038548, A364388, A364389, A364420.