A161842 Partial sums of A161841.

2, 4, 6, 10, 12, 16, 18, 22, 26, 30, 32, 38, 40, 44, 48, 54, 56, 62, 64, 70, 74, 78, 80, 88, 92, 96, 100, 106, 108, 116, 118, 124, 128, 132, 136, 146, 148, 152, 156, 164, 166, 174, 176, 182, 188, 192, 194, 204, 208, 214, 218, 224, 226, 234, 238, 246

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Michael Penn, This is always even??, YouTube video, 2020.

Formula

a(n) = 2*A094820(n).

a(n) = Sum_{i=1..n} (1 + A008836(i))*floor(n/i)). - Enrique Pérez Herrero, Jul 10 2012

a(n) ~ (log(n) + 2*gamma - 1)*n + sqrt(n), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 01 2021

Prog

(PARI) a(n) = sum(i=1, n, floor(n/i)) + sqrtint(n) \\ David A. Corneth, Dec 17 2020
(PARI) first(n) = {my(res = vector(n), t = 0); for(i = 1, n, t+=(numdiv(i)+issquare(i)); res[i] = t ); res } \\ David A. Corneth, Dec 17 2020

Crossrefs

Cf. A001620, A008836, A038548, A094820, A161841.

Sequence in context: A355643 A107304 A082417 * A249434 A249425 A085477

Adjacent sequences: A161839 A161840 A161841 * A161843 A161844 A161845

Keyword

nonn,easy

Author

Omar E. Pol, Jun 23 2009

Status

approved