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

Author

Omar E. Pol, Jun 23 2009

Keywords

• nonn
• easy

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Michael Penn, This is always even??, YouTube video, 2020.

Crossrefs

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

Programs

Mathematica

Accumulate[2*Ceiling[DivisorSigma[0, Range[100]]/2]] (* Paolo Xausa, Feb 05 2025 *)

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

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