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A359270
Number of divisors of 5*n-3 of form 5*k+3.
6
0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 3, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 0, 3, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 1, 4, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 4, 0, 1, 1, 1, 0, 3, 0, 2, 1, 0, 0, 2, 1, 0, 2, 3, 0, 1, 0, 1, 1, 0, 0, 5, 1, 1, 1
OFFSET
1,15
COMMENTS
Also number of divisors of 5*n-3 of form 5*k+4.
LINKS
FORMULA
a(n) = A001878(5*n-3) = A001899(5*n-3).
G.f.: Sum_{k>0} x^(3*k)/(1 - x^(5*k-1)).
G.f.: Sum_{k>0} x^(4*k-1)/(1 - x^(5*k-2)).
MATHEMATICA
a[n_] := DivisorSum[5*n-3, 1 &, Mod[#, 5] == 3 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-3, d, d%5==3);
(PARI) a(n) = sumdiv(5*n-3, d, d%5==4);
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(5*k-1)))))
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(4*k-1)/(1-x^(5*k-2)))))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 23 2022
STATUS
approved