A344885 - OEIS

%I #10 Jun 30 2021 19:48:31

%S 1,1,1,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,

%T 0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,1,0,0,1,0,

%U 0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0,0

%N a(n) = 1 if A011772(n) is equal to A344878(n), otherwise 0; characteristic function of A344979.

%H Antti Karttunen, <a href="/A344885/b344885.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = 1 if A344976(n) = 0, otherwise 0.

%F A010055(n) <= a(n) <= A344884(n).

%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 A344878(n) = if(1==n,n, my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^(f[2, i]+(2==f[1, i]))-1))));

%o A344885(n) = (A344878(n)==A011772(n));

%Y Characteristic function of A344979.

%Y Cf. A010055, A011772, A344878, A344880, A344884, A344976.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 05 2021