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A293896
Number of proper divisors of n of the form 3k+2.
7
0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 4, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 1, 2, 3, 0, 2, 0, 3, 0, 1, 0, 3, 1, 2, 0, 2, 1, 4, 0, 2, 0, 1, 1, 2, 1, 2, 0, 4, 0, 2, 0, 2, 2, 1, 1, 4, 0, 2, 0, 2, 0, 2, 1, 3, 0, 2, 1, 4, 0, 2, 0, 3, 2
OFFSET
1,10
LINKS
R. A. Smith and M. V. Subbarao, The average number of divisors in an arithmetic progression, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
FORMULA
a(n) = A001822(n) - [n == 2 (mod 3)].
G.f.: Sum_{k>=1} x^(6*k-2) / (1 - x^(3*k-1)). - 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(2,3) - (2 - gamma)/3 = A256843 - (2 - A001620)/3 = -0.401054... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023
MATHEMATICA
Table[DivisorSum[n, 1 &, And[Mod[#, 3] == 2, # != n] &], {n, 105}] (* Michael De Vlieger, Nov 08 2017 *)
PROG
(PARI) A293896(n) = sumdiv(n, d, (d<n)*(2==(d%3)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Nov 06 2017
STATUS
approved