A114006 - OEIS

%I #21 Feb 23 2020 16:27:58

%S 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,

%T -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,

%U -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

%N Row sums of number triangle A114004.

%C A signed version of A050328.

%H Antti Karttunen, <a href="/A114006/b114006.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A008836(n) * A050328(n). - _Antti Karttunen_, May 27 2017

%F a(1) = 1; a(n) = Sum_{d|n, d < n} mu(n/d) * a(d). - _Ilya Gutkovskiy_, Feb 23 2020

%t 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 *)

%o (PARI)

%o A050328(n) = if(1==n,n,sumdiv(n,d,if((d<n && issquarefree(n/d)),A050328(d),0)));

%o A114006(n) = ((-1)^bigomega(n) * A050328(n)); \\ _Antti Karttunen_, May 27 2017

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

%K easy,sign

%O 1,6

%A _Paul Barry_, Nov 12 2005

%E More terms, incorrect formulas replaced by a correct one - _Antti Karttunen_, May 27 2017