A344874 - OEIS

%I #9 Jun 30 2021 10:33:24

%S 0,-2,0,-4,0,-1,0,-8,0,0,0,-2,0,-1,3,-16,0,0,0,-3,6,-1,0,-1,0,0,0,11,

%T 0,-7,0,-32,9,0,10,16,0,-1,12,13,0,-8,0,-2,23,-1,0,-2,0,0,15,-3,0,-1,

%U 30,-6,18,0,0,9,0,-1,21,-64,23,9,0,32,21,4,0,-7,0,0,24,-2,39,12,0,-4,0,0,0,-12,30,-1,27,38,0,-3,59

%N a(n) = A047994(n) - A011772(n).

%H Antti Karttunen, <a href="/A344874/b344874.txt">Table of n, a(n) for n = 1..16384</a>

%o (PARI)

%o A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772

%o A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };

%o A344874(n) = (A047994(n)-A011772(n));

%Y Cf. A011772, A047994.

%Y Cf. also A344763, A344765, A344876.

%K sign

%O 1,2

%A _Antti Karttunen_, Jun 03 2021