A123707 a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1).

1, 0, 1, 3, 7, 14, 31, 60, 126, 248, 511, 1005, 2047, 4064, 8183, 16320, 32767, 65394, 131071, 261885, 524255, 1048064, 2097151, 4193220, 8388600, 16775168, 33554304, 67104765, 134217727, 268427002, 536870911, 1073725440, 2147483135

Offset: 1

Author

Paul D. Hanna, Oct 09 2006

Keywords

• nonn

Comments

Triangle A123706 is the matrix inverse of triangle A010766(n,k) = [n/k].

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A123706, A123708, A123709.

Programs

Mathematica

t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Oct 26 2017 *)

PARI

{a(n)=sum(k=1,n,(matrix(n,n,r,c,if(r>=c,floor(r/c)))^-1)[n,k]*2^(k-1))}

Formula

G.f.: Sum_{k>=1} mu(k) * x^k * (1 - x^k) / (1 - 2*x^k). - Ilya Gutkovskiy, Feb 06 2020

a(n) ~ 2^(n-2). - Vaclav Kotesovec, May 03 2025