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

%I A158568 #22 Oct 10 2021 06:12:03
%S A158568 1,1,3,5,10,20,37,70,127,231,413,746,1307,2295,4010,6957,12031,20712,
%T A158568 35514,60718,103500,175989,298539,505399,853777,1439856,2424299,
%U A158568 4075479,6841787,11470592,19207624,32126763,53678285
%N A158568 a(n) = Sum_{i=1..Fibonacci(n)} sigma_0(i) where sigma_0(n) is A000005(n).
%H A158568 Chai Wah Wu, <a href="/A158568/b158568.txt">Table of n, a(n) for n = 1..106</a>
%p A158568 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
%t A158568 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 *)
%o A158568 (PARI) a(n) = sum(k=1, fibonacci(n), numdiv(k)); \\ _Michel Marcus_, Feb 12 2019
%o A158568 (Python)
%o A158568 from math import isqrt
%o A158568 def A153568(n):
%o A158568     a, b, = 0, 1
%o A158568     for _ in range(n): a, b = b, a+b
%o A158568     return (lambda m: 2*sum(a//k for k in range(1, m+1))-m*m)(isqrt(a)) # _Chai Wah Wu_, Oct 09 2021
%Y A158568 Cf. A000005, A000045, A006218, A085831, A062550, A153876, A153817, A153816.
%K A158568 nonn
%O A158568 1,3
%A A158568 _Ctibor O. Zizka_, Mar 21 2009
%E A158568 a(16)-a(33) from _Nathaniel Johnston_, May 09 2011