A218445 a(n) = Sum_{k>=0} floor(n/(5*k + 2)).

0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 8, 8, 10, 10, 11, 12, 13, 13, 14, 15, 17, 17, 19, 19, 20, 21, 23, 23, 24, 24, 26, 26, 28, 29, 31, 32, 33, 33, 34, 34, 37, 37, 39, 39, 40, 41, 43, 44, 45, 46, 48, 48, 50, 50, 52, 53, 54, 54, 56, 56, 58, 59, 61, 61, 63, 64, 66, 66, 68, 68, 71, 71, 73, 73, 74, 76, 77, 77, 78

Offset

0,5

Links

Seiichi Manyama, 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

a(n) = 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, Apr 20 2025

Mathematica

Table[Sum[Floor[n/(5k+2)], {k, 0, n}], {n, 0, 80}] (* Harvey P. Dale, Dec 08 2022 *)

Prog

(PARI) a(n)=sum(k=0, n\5, (n\(5*k+2)))
(Maxima) A218445[n]:=sum(floor(n/(5*k+2)), k, 0, n)$
makelist(A218445[n], n, 0, 80); /* Martin Ettl, Oct 29 2012 */

Crossrefs

Partial sums of A001877.

Cf. A218444, A218446, A218447.

Cf. A001620, A256780.

Sequence in context: A065855 A236863 A242976 * A034137 A156351 A057561

Adjacent sequences: A218442 A218443 A218444 * A218446 A218447 A218448

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 28 2012

Status

approved