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A001876
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Number of divisors of n of the form 5k+1; a(0)=0.
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18
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0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 4, 1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 1
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OFFSET
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0,7
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} x^(5n+1)/(1-x^(5n+1)).
G.f.: Sum_{n>=1} x^n/(1-x^(5*n)). - Joerg Arndt, Jan 30 2011
Sum_{k=1..n} a(k) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,5) - (1 - gamma)/5 = A256779 - (1 - A001620)/5 = 0.651363... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
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MATHEMATICA
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CoefficientList[ Series[ Together[ Sum[ x^n/(1 - x^(5n)), {n, 110}]], {x, 0, 110}], x] (* Robert G. Wilson v, Jan 31 2011 *)
a[n_] := DivisorSum[n, 1 &, Mod[#, 5] == 1 &]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Nov 25 2023 *)
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PROG
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(PARI) a(n) = if(n==0, 0, sumdiv(n, d, (d % 5) == 1)); \\ Michel Marcus, Feb 25 2021
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CROSSREFS
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For numbers of divisors of n of the form 5k+i (i=1, 2, 3, 4) see: this sequence, A001877, A001878, A001899.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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