A364420 Number of divisors of n of the form 5*k+4 that are at most sqrt(n).

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

Offset

1,108

Links

Table of n, a(n) for n=1..108.

Formula

G.f.: Sum_{k>=0} x^(5*k+4)^2 / (1 - x^(5*k+4)).

Mathematica

Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{4}, Mod[#, 5]] &)], {n, 108}]
nmax = 108; CoefficientList[Series[Sum[x^(5 k + 4)^2/(1 - x^(5 k + 4)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A001899, A038548, A364388, A364389, A364419.

Sequence in context: A336835 A353418 A361161 * A368006 A374061 A374276

Adjacent sequences: A364417 A364418 A364419 * A364421 A364422 A364423

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 23 2023

Status

approved