A062550 a(n) = Sum_{k = 1..2n} floor(2n/k).

0, 3, 8, 14, 20, 27, 35, 41, 50, 58, 66, 74, 84, 91, 101, 111, 119, 127, 140, 146, 158, 168, 176, 186, 198, 207, 217, 227, 239, 247, 261, 267, 280, 292, 300, 312, 326, 332, 344, 356, 368, 377, 391, 399, 411, 425, 435, 443, 459, 467, 482, 492, 502, 514, 528

Offset: 0

Author

Henry Bottomley, Jun 26 2001

Keywords

• nonn

Comments

The sequence A006218 : Sum_{i=1..n} floor(n/i) = Sum_{i=1..n} sigma_0(i). Sigma_0(i) is A000005. Sequences of the type : Sum_{i=1..f(n)} floor(f(n)/i)= Sum_{i=1..f(n)} sigma_0(i). This sequence a(n)= A006218(2*n). [Ctibor O. Zizka, Mar 21 2009]

For n > 0: row sums of the triangle in A013942. - Reinhard Zumkeller, Jun 04 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A013942, A156745, A085831, A153816, A153817, A153876.

Programs

Haskell

a062550 0 = 0
a062550 n = sum $ a013942_row n  -- Reinhard Zumkeller, Jun 04 2013

Mathematica

Table[Total[Floor[2*n/Range[2*n]]], {n, 0, 100}] (* T. D. Noe, Jun 12 2013 *)

PARI

a(n) = sum(k=1, 2*n, (2*n)\k); \\ Michel Marcus, Oct 09 2021

Python

from math import isqrt
def A062550(n): return (lambda m: 2*sum(2*n//k for k in range(1, m+1))-m*m)(isqrt(2*n)) # Chai Wah Wu, Oct 09 2021

Formula

a(n) = A006218(2n) = A056549(n)+A006218(n) = a(n-1)+A000005(2n-1)+A000005(2n)

Extensions

Data corrected for n > 30 by Reinhard Zumkeller, Jun 04 2013