A156745 a(n) = Sum_{k=1..n} floor((n+k)/k) = n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also a(n) = n + A006218(n).

2, 5, 8, 12, 15, 20, 23, 28, 32, 37, 40, 47, 50, 55, 60, 66, 69, 76, 79, 86, 91, 96, 99, 108, 112, 117, 122, 129, 132, 141, 144, 151, 156, 161, 166, 176, 179, 184, 189, 198, 201, 210, 213, 220, 227, 232, 235, 246, 250, 257, 262, 269, 272, 281, 286, 295, 300

Offset: 1

Author

Ctibor O. Zizka, Feb 14 2009

Keywords

• easy
• nonn

Comments

Generalized sequence b(n) = Sum_{k=1..n} floor((n+k*t)/k) = t*n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also b(n) = t*n + A006218(n).

Partial sums of A334954. - Omar E. Pol, Sep 26 2020

Crossrefs

Cf. A000005, A006218, A153818, A118014, A002541, A334954.

Programs

PARI

a(n) = n + sum(k=1, n, numdiv(k)); \\ Michel Marcus, Oct 02 2020

Python

from math import isqrt
def A156745(n): return n-(s:=isqrt(n))**2+(sum(n//k for k in range(1,s+1))<<1) # Chai Wah Wu, Oct 23 2023

Formula

a(n) = 2*n + Sum_{k=1..floor(n/2)} floor((n-k)/k). - Wesley Ivan Hurt, Dec 25 2020

a(n) = A005843(n) + A002541(n), after Wesley Ivan Hurt. - Omar E. Pol, Dec 25 2020

Extensions

More terms from Eric M. Schmidt, Feb 28 2014