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A001461 Partial sums of A006206.

%I A001461 #29 Apr 22 2020 18:30:19
%S A001461 1,2,3,4,6,8,12,17,25,36,54,79,119,177,267,402,612,928,1420,2170,3334,
%T A001461 5125,7911,12216,18926,29346,45610,70960,110610,172577,269685,421830,
%U A001461 660648,1035603,1625123
%N A001461 Partial sums of A006206.
%H A001461 James Spahlinger, <a href="/A001461/b001461.txt">Table of n, a(n) for n = 1..1000</a>
%H A001461 D. J. Broadhurst, <a href="https://arxiv.org/abs/hep-th/9604128">On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory</a>, arXiv:hep-th/9604128, 1996.
%p A001461 b := proc(n) local sum; sum := 0; for d in divisors(n) do sum := sum + mobius(n/d)*(fibonacci(d+1)+fibonacci(d-1)) od; RETURN(sum/n); end; A001461 := proc(n) local i; add(b(i),i=1..n); end;
%t A001461 b[n_] := Sum[MoebiusMu[n/d] (Fibonacci[d + 1] + Fibonacci[d - 1]), {d, Divisors[n]}]/n; Accumulate[Table[b[n], {n, 35}]] (* _Jean-François Alcover_, Dec 02 2011 *)
%o A001461 (Haskell)
%o A001461 a001461 n = a001461_list !! (n-1)
%o A001461 a001461_list = scanl1 (+) a006206_list -- _Reinhard Zumkeller_, Jun 01 2013
%o A001461 (Sage)
%o A001461 def a(n):
%o A001461     return sum((fibonacci(d + 1) + fibonacci(d - 1)) * moebius(n // d) for d in divisors(n)) // n
%o A001461 def b(n):
%o A001461     return sum(a(i) for i in range(1, n + 1))
%K A001461 nonn,nice,easy
%O A001461 1,2
%A A001461 _N. J. A. Sloane_, _David Broadhurst_