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A083916
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Number of divisors of n that are congruent to 6 modulo 10.
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11
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0
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OFFSET
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1,36
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(6,10) - (1 - gamma)/10 = -0.118475..., gamma(6,10) = -(psi(3/5) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023
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MATHEMATICA
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Table[Count[Divisors[n], _?(Mod[#, 10]==6&)], {n, 110}] (* Harvey P. Dale, Oct 16 2013 *)
a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 6 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d % 10 == 6); \\ Amiram Eldar, Dec 30 2023
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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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