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A359233
Number of divisors of 5*n-1 of form 5*k+1.
11
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 3, 1, 3, 1, 1, 2, 4, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 1, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1
OFFSET
1,5
COMMENTS
Also number of divisors of 5*n-1 of form 5*k+4.
LINKS
FORMULA
a(n) = A001876(5*n-1) = A001899(5*n-1).
G.f.: Sum_{k>0} x^k/(1 - x^(5*k-1)).
G.f.: Sum_{k>0} x^(4*k-3)/(1 - x^(5*k-4)).
MATHEMATICA
a[n_] := DivisorSum[5*n-1, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
PROG
(PARI) a(n) = sumdiv(5*n-1, d, d%5==1);
(PARI) a(n) = sumdiv(5*n-1, d, d%5==4);
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(5*k-1))))
(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(4*k-3)/(1-x^(5*k-4))))
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2022
STATUS
approved