A001878 Number of divisors of n of the form 5k+3; a(0) = 0.

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

Offset

0,19

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

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

G.f.: Sum_{n>=0} x^(5*n+3)/(1 - x^(5*n+3)).

G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(5*k)). - Ilya Gutkovskiy, Sep 11 2019

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

Mathematica

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 *)

Prog

(PARI) a(n) = if (n==0, 0, sumdiv(n, d, (d % 5)==3)); \\ Michel Marcus, Feb 28 2021

Crossrefs

Cf. A001876, A001877, A001899.

Cf. A001620, A256848.

Sequence in context: A035168 A255647 A119241 * A056558 A320808 A338203

Adjacent sequences: A001875 A001876 A001877 * A001879 A001880 A001881

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved