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A364358
Number of divisors of n of the form 4*k+1 that are at most sqrt(n).
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2
OFFSET
1,25
FORMULA
G.f.: Sum_{k>=0} x^(4*k+1)^2 / (1 - x^(4*k+1)).
MATHEMATICA
Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{1}, Mod[#, 4]] &)], {n, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(4 k + 1)^2/(1 - x^(4 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 21 2023
STATUS
approved