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A293895
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Number of proper divisors of n of the form 3k+1.
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7
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0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 1, 1, 3, 2, 3, 1, 3, 1, 1, 1, 4, 2, 1, 1, 3, 1, 2, 2, 3, 2, 2, 1, 3, 1, 3, 1, 2, 1, 2, 2, 3, 2, 2, 1, 5, 1, 1, 1, 4, 1, 2, 1, 3, 1, 2, 3, 3, 2, 1, 2, 3, 1, 3, 1, 4, 1, 2, 1, 4, 2
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OFFSET
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1,8
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LINKS
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FORMULA
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a(n) = A001817(n) - [n == 1 (mod 3)].
G.f.: Sum_{k>=1} x^(6*k-4) / (1 - x^(3*k-2)). - Ilya Gutkovskiy, Apr 14 2021
Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,3) - (2 - gamma)/3 = A256425 - (2 - A001620)/3 = 0.203545... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
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MATHEMATICA
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Table[DivisorSum[n, 1 &, And[Mod[#, 3] == 1, # != n] &], {n, 105}] (* Michael De Vlieger, Nov 08 2017 *)
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PROG
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(PARI) A293895(n) = sumdiv(n, d, (d<n)*(1==(d%3)));
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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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