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

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

Author

Ctibor O. Zizka, Mar 21 2009

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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 *)

PARI

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

Python

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

Extensions

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