A153817 -id:A153817 - cp's OEIS frontend

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

Henry Bottomley, Jun 26 2001

nonn

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

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

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

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

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

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

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

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

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

A158568 a(n) = Sum_{i=1..Fibonacci(n)} sigma_0(i) where sigma_0(n) is A000005(n).

Original entry on oeis.org

1, 1, 3, 5, 10, 20, 37, 70, 127, 231, 413, 746, 1307, 2295, 4010, 6957, 12031, 20712, 35514, 60718, 103500, 175989, 298539, 505399, 853777, 1439856, 2424299, 4075479, 6841787, 11470592, 19207624, 32126763, 53678285

Offset: 1

Ctibor O. Zizka, Mar 21 2009

nonn

Chai Wah Wu, Table of n, a(n) for n = 1..106

Cf. A000005, A000045, A006218, A085831, A062550, A153876, A153817, A153816.

with(combinat):with(numtheory): A158568 := proc(n) return add(tau(i),i=1..fibonacci(n)): end: seq(A158568(n),n=1..20); # Nathaniel Johnston, May 09 2011

Module[{nn=33,f,d},f=Fibonacci[nn];d=DivisorSigma[0,Range[f]];Table[ Total[ Take[d,n]],{n,Fibonacci[Range[nn]]}]] (* Harvey P. Dale, Apr 29 2018 *)

a(n) = sum(k=1, fibonacci(n), numdiv(k)); \\ Michel Marcus, Feb 12 2019

from math import isqrt
def A153568(n):
    a, b, = 0, 1
    for _ in range(n): a, b = b, a+b
    return (lambda m: 2*sum(a//k for k in range(1, m+1))-m*m)(isqrt(a)) # Chai Wah Wu, Oct 09 2021

a(16)-a(33) from Nathaniel Johnston, May 09 2011

cp's OEIS Frontend

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

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