A001877 Number of divisors of n of the form 5k+2; a(0) = 0.

0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 3, 0, 2, 0, 1, 1, 2, 1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 3, 0, 2, 0, 1, 2, 1, 0, 1, 1, 2, 0, 4, 1, 1, 1

Offset

0,13

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^(5n+2)/(1-x^(5n+2)).

G.f.: Sum_(n>=1} x^(2*n)/(1-x^(5*n))). - Joerg Arndt, Jan 30 2011

Sum_{k=1..n} a(k) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(2,5) - (1 - gamma)/5 = A256780 - (1 - A001620)/5 = 0.105832... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

Mathematica

Join[{0}, Table[d = Divisors[n]; Length[Select[d, Mod[#, 5] == 2 &]], {n, 100}]] (* T. D. Noe, Aug 10 2012 *)
Table[Count[Divisors[n], _?(Mod[#, 5]==2&)], {n, 0, 90}] (* Harvey P. Dale, May 20 2017 *)

Prog

(PARI) a(n) = if (n==0, 0, sumdiv(n, d, (d % 5)==2)); \\ Michel Marcus, Feb 28 2021

Crossrefs

Cf. A001876, A001878, A001899.

Cf. A001620, A256780.

Sequence in context: A358331 A277142 A240592 * A339896 A112712 A026608

Adjacent sequences: A001874 A001875 A001876 * A001878 A001879 A001880

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved