A218446 a(n) = Sum_{k>=0} floor(n/(5*k + 3)).

0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 10, 10, 10, 11, 11, 12, 14, 14, 15, 16, 17, 17, 18, 18, 19, 21, 21, 21, 23, 23, 24, 26, 27, 27, 28, 29, 29, 30, 31, 31, 34, 34, 34, 35, 36, 37, 39, 39, 41, 42, 43, 43, 44, 44, 44, 46, 47, 48, 50, 50, 51, 53, 53, 53, 56, 57, 57, 58, 59, 59, 62, 62, 63

Offset

0,7

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(3,5) - (1 - gamma)/5 = A256848 - (1 - A001620)/5 = -0.0983206... (Smith and Subbarao, 1981). - Amiram Eldar, Apr 20 2025

Mathematica

Accumulate[Table[Count[Divisors[n], _?(Mod[#, 5]==3&)], {n, 0, 90}]] (* Harvey P. Dale, Nov 08 2012 *)

Prog

(PARI) a(n)=sum(k=0, n, (n\(5*k+3)))
(Maxima) A218446[n]:=sum(floor(n/(5*k+3)), k, 0, n)$
makelist(A218446[n], n, 0, 80); /* Martin Ettl, Oct 29 2012 */

Crossrefs

Partial sums of A001878.

Cf. A218444, A218445, A218447.

Cf. A001620, A256848.

Sequence in context: A046699 A239105 A302255 * A362965 A102548 A343174

Adjacent sequences: A218443 A218444 A218445 * A218447 A218448 A218449

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 28 2012

Status

approved