A293896 Number of proper divisors of n of the form 3k+2.

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

Antti Karttunen, Table of n, a(n) for n = 1..20000

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

Cf. A001620, A001822, A256843, A293895, A293898, A293899.

Sequence in context: A328616 A260736 A342656 * A066416 A292342 A091991

Adjacent sequences: A293893 A293894 A293895 * A293897 A293898 A293899

Keyword

nonn,easy

Author

Antti Karttunen, Nov 06 2017

Status

approved