A114005 - OEIS

%I #15 Feb 23 2020 16:27:51

%S 1,-2,-2,2,-2,6,-2,-2,2,6,-2,-10,-2,6,6,2,-2,-10,-2,-10,6,6,-2,14,2,6,

%T -2,-10,-2,-26,-2,-2,6,6,6,26,-2,6,6,14,-2,-26,-2,-10,-10,6,-2,-18,2,

%U -10,6,-10,-2,14,6,14,6,6,-2,62,-2,6,-10,2,6,-26,-2,-10,6,-26,-2,-50,-2,6,-10,-10,6,-26,-2,-18,2,6,-2,62,6,6,6,14,-2,62,6,-10,6,6,6

%N First column of number triangle A114004.

%C Moebius transform of A114006. - _Mats Granvik_, Jan 02 2009

%H Antti Karttunen, <a href="/A114005/b114005.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 1, for n > 1, a(n) = 2*A114006(n). - Corrected by _Antti Karttunen_, May 27 2017

%F a(1) = 1; a(n) = -2 * Sum_{d|n, d < n} a(d). - _Ilya Gutkovskiy_, Feb 23 2020

%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));

%o A114005(n) = if(1==n,n,2*A114006(n)); \\ _Antti Karttunen_, May 27 2017

%Y Cf. A050328, A114006.

%K easy,sign

%O 1,2

%A _Paul Barry_, Nov 12 2005

%E More terms from _Antti Karttunen_, May 27 2017