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A364107
Expansion of Sum_{k>0} k * x^(4*k) / (1 - x^(5*k-1)).
4
0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 5, 2, 0, 0, 6, 0, 0, 0, 7, 0, 5, 0, 8, 0, 0, 0, 9, 0, 0, 6, 10, 0, 0, 0, 14, 0, 0, 0, 19, 0, 0, 0, 13, 0, 0, 0, 14, 8, 7, 0, 15, 0, 0, 0, 16, 0, 9, 0, 17, 0, 0, 0, 26, 0, 0, 10, 19, 4, 0, 0, 20, 0, 0, 0, 32, 0, 9, 0, 22, 0, 0, 0, 23, 12, 0, 0, 33, 0, 0, 0
OFFSET
1,8
FORMULA
a(n) = (1/5) * Sum_{d | 5*n-4, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k) / (1 - x^(5*k-1))^2.
MATHEMATICA
a[n_] := DivisorSum[5*n - 4, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-4, d, (d%5==4)*(d+1))/5;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 05 2023
STATUS
approved