A335909 - OEIS

%I #16 Jul 20 2020 02:07:58

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

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

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

%N Parity of A323173: a(n) = A000035(A323173(n)).

%H Antti Karttunen, <a href="/A335909/b335909.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A053866(A122111(n)).

%o (PARI)

%o A053866(n) = if( n<1, 0, issquare(n) || issquare(2*n));

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A335909(n) = A053866(A122111(n));

%Y Parity of A323173. Characteristic function of A336119.

%Y Cf. A000035, A053866, A122111.

%Y Cf. also A166486.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 07 2020