A001036 - OEIS

%I M1067 N0403 #30 Aug 24 2023 02:31:43

%S 1,2,4,7,13,22,40,70,126,225,411,746,1376,2537,4719,8799,16509,31041,

%T 58635,111012,210870,401427,766149,1465019,2807195,5387990,10358998,

%U 19945393,38458183,74248450,143522116,277737796,538038782,1043325197

%N Partial sums of A001037, omitting A001037(1).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. A. Harrison, <a href="https://www.jstor.org/stable/2946369">On the classification of Boolean functions by the general linear and affine groups</a>, J. Soc. Indust. Appl. Math. 12 (1964), 285-299.

%F a(n) = A062692(n)-1. - _Gabriele Fici_, Feb 02 2011

%F G.f.: -x/(1 - x) + (1/(1 - x)) * Sum_{k>=1} mu(k)*log(1/(1 - 2*x^k))/k. - _Ilya Gutkovskiy_, Nov 11 2019

%t f[n_] := DivisorSum[n, MoebiusMu[#] * 2^(n/#) &] / n; Accumulate[Array[f, 30]] - 1 (* _Amiram Eldar_, Aug 24 2023 *)

%Y Cf. A001037, A062692.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_, Oct 11 2000