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

1,6

Comments

A signed version of A050328.

Links

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

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

Mathematica

a050328[n_]:=If[n==1, n, Sum[If[(d<n && SquareFreeQ[n/d]), a050328[d], 0], {d, Divisors[n]}]]; a[n_]:=(-1)^PrimeOmega[n]*a050328[n]; Table[a[n], {n, 100}] (* Indranil Ghosh, May 27 2017 *)

Prog

(PARI)
A050328(n) = if(1==n, n, sumdiv(n, d, if((d<n && issquarefree(n/d)), A050328(d), 0)));
A114006(n) = ((-1)^bigomega(n) * A050328(n)); \\ Antti Karttunen, May 27 2017

Crossrefs

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

Sequence in context: A029356 A334019 A291448 * A050328 A191278 A363085

Adjacent sequences: A114003 A114004 A114005 * A114007 A114008 A114009

Keyword

easy,sign

Author

Paul Barry, Nov 12 2005

Extensions

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

Status

approved