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A363929
Expansion of Sum_{k>0} x^(4*k) / (1 - x^(5*k))^2.
4
0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 0, 1, 0, 2, 4, 1, 0, 0, 0, 6, 0, 0, 2, 4, 6, 0, 0, 1, 0, 7, 0, 3, 0, 4, 8, 1, 0, 3, 0, 10, 2, 0, 0, 6, 10, 0, 0, 1, 0, 13, 0, 4, 4, 6, 12, 1, 0, 0, 2, 14, 0, 0, 0, 8, 14, 3, 0, 8, 0, 15, 0, 5, 0, 8, 16, 1, 2, 0, 0, 21, 0, 0, 6, 10, 18, 2, 0, 1, 0, 19, 4, 6, 0, 13, 22, 1, 0, 7, 0, 22, 0, 0, 0, 14, 22, 0, 0
OFFSET
1,9
LINKS
FORMULA
a(n) = (1/5) * Sum_{d|n, d==4 mod 5} (d+1) = (A001899(n) + A284103(n))/5.
G.f.: Sum_{k>0} k * x^(5*k-1) / (1 - x^(5*k-1)).
MATHEMATICA
a[n_] := DivisorSum[n, # + 1 &, Mod[#, 5] == 4 &] / 5; Array[a, 100] (* Amiram Eldar, Jun 28 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%5==4)*(d+1))/5;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 28 2023
STATUS
approved