A001036 Partial sums of A001037, omitting A001037(1).

1, 2, 4, 7, 13, 22, 40, 70, 126, 225, 411, 746, 1376, 2537, 4719, 8799, 16509, 31041, 58635, 111012, 210870, 401427, 766149, 1465019, 2807195, 5387990, 10358998, 19945393, 38458183, 74248450, 143522116, 277737796, 538038782, 1043325197

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964), 285-299.

Crossrefs

Cf. A001037, A062692.

Programs

Mathematica

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

Formula

a(n) = A062692(n)-1. - Gabriele Fici, Feb 02 2011

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

Extensions

More terms from David W. Wilson, Oct 11 2000