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A001878
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Number of divisors of n of the form 5k+3; a(0) = 0.
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16
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0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 0, 3, 0, 0, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 0, 1, 2, 0, 0, 3, 1, 0, 1, 1, 0, 3, 0, 1, 1, 0, 1, 2, 0, 1, 1
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OFFSET
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0,19
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} x^(5*n+3)/(1 - x^(5*n+3)).
Sum_{k=1..n} a(k) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,5) - (1 - gamma)/5 = A256848 - (1 - A001620)/5 = -0.0983206... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
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MATHEMATICA
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Join[{0}, Table[d = Divisors[n]; Length[Select[d, Mod[#, 5] == 3 &]], {n, 100}]] (* T. D. Noe, Aug 10 2012 *)
Table[Count[Divisors[n], _?(Mod[#, 5]==3&)], {n, 0, 90}] (* Harvey P. Dale, Nov 08 2012 *)
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PROG
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(PARI) a(n) = if (n==0, 0, sumdiv(n, d, (d % 5)==3)); \\ Michel Marcus, Feb 28 2021
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CROSSREFS
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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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