A114006 Row sums of number triangle A114004.

1, -1, -1, 1, -1, 3, -1, -1, 1, 3, -1, -5, -1, 3, 3, 1, -1, -5, -1, -5, 3, 3, -1, 7, 1, 3, -1, -5, -1, -13, -1, -1, 3, 3, 3, 13, -1, 3, 3, 7, -1, -13, -1, -5, -5, 3, -1, -9, 1, -5, 3, -5, -1, 7, 3, 7, 3, 3, -1, 31, -1, 3, -5, 1, 3, -13, -1, -5, 3, -13, -1, -25, -1, 3, -5, -5, 3, -13, -1, -9, 1, 3, -1, 31, 3, 3, 3, 7, -1, 31, 3, -5, 3, 3, 3, 11

Offset: 1

Author

Paul Barry, Nov 12 2005

Keywords

• easy
• sign

Comments

A signed version of A050328.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008836, A008966, A050328, A114004, A114005.

Programs

Mathematica

a050328[n_]:=If[n==1, n, Sum[If[(dIndranil Ghosh, May 27 2017 *)

PARI

A050328(n) = if(1==n,n,sumdiv(n,d,if((dA050328(d),0)));
A114006(n) = ((-1)^bigomega(n) * A050328(n)); \\ Antti Karttunen, May 27 2017

Formula

a(n) = A008836(n) * A050328(n). - Antti Karttunen, May 27 2017

a(1) = 1; a(n) = Sum_{d|n, d < n} mu(n/d) * a(d). - Ilya Gutkovskiy, Feb 23 2020

Extensions

More terms, incorrect formulas replaced by a correct one - Antti Karttunen, May 27 2017