A218442 a(n) = Sum_{k=0..n} floor(n/(3*k + 1)).

0, 1, 2, 3, 5, 6, 7, 9, 11, 12, 14, 15, 17, 19, 21, 22, 25, 26, 27, 29, 32, 34, 36, 37, 39, 41, 43, 44, 48, 49, 51, 53, 56, 57, 59, 61, 63, 65, 67, 69, 73, 74, 76, 78, 81, 82, 84, 85, 88, 91, 94, 95, 99, 100, 101, 103, 107, 109, 111, 112, 115, 117, 119, 121, 125, 127, 129, 131, 134, 135, 139, 140, 142, 144, 146, 148, 152

Offset

0,3

Links

Amiram Eldar, 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)/3 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

Mathematica

d[n_] := DivisorSum[n, 1 &, Mod[#, 3] == 1 &]; d[0] = 0; Accumulate@Array[d, 100, 0] (* Amiram Eldar, Nov 25 2023 *)

Prog

(PARI) a(n)=sum(k=0, n\3, (n\(3*k+1)))
(Maxima) A218442[n]:=sum(floor(n/(3*k+1)), k, 0, n)$
makelist(A218442[n], n, 0, 80); /* Martin Ettl, Oct 29 2012 */

Crossrefs

Partial sums of A001817.

Cf. A001620, A218443, A256425.

Sequence in context: A282131 A114148 A349690 * A255057 A349150 A354525

Adjacent sequences: A218439 A218440 A218441 * A218443 A218444 A218445

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 28 2012

Status

approved