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A363903
Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^2.
6
1, 1, 1, 1, 3, 1, 1, 1, 4, 3, 1, 1, 5, 1, 3, 1, 6, 4, 1, 3, 7, 1, 1, 1, 10, 5, 4, 1, 9, 3, 1, 1, 10, 6, 3, 4, 11, 1, 5, 3, 12, 7, 1, 1, 18, 1, 1, 1, 14, 10, 6, 5, 15, 4, 3, 1, 16, 9, 1, 3, 17, 1, 10, 1, 24, 10, 1, 6, 19, 3, 1, 4, 20, 11, 10, 1, 21, 5, 1, 3, 25, 12, 1, 7, 30, 1, 9, 1, 24, 18, 5, 1, 25, 1, 3, 1
OFFSET
1,5
LINKS
FORMULA
a(n) = (1/4) * Sum_{d|n, d==1 mod 4} (d+3) = (3 * A001826(n) + A050449(n))/4.
G.f.: Sum_{k>0} k * x^(4*k-3) / (1 - x^(4*k-3)).
MATHEMATICA
a[n_] := DivisorSum[n, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%4==1)*(d+3))/4;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 27 2023
STATUS
approved