A344884 - OEIS

%I #9 Jun 30 2021 10:33:02

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

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

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

%N a(n) = 1 if A011772(n) divides A344875(n), otherwise 0; characteristic function of A344974.

%H Antti Karttunen, <a href="/A344884/b344884.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) >= A344885(n) >= A010055(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 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };

%o A344884(n) = !(A344875(n)%A011772(n));

%Y Characteristic function of A344974.

%Y Cf. A010055, A011772, A344875, A344880, A344885.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 05 2021