A336121 - OEIS

%I #9 Jul 17 2020 22:57:33

%S 0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,2,0,2,0,1,0,1,0,2,1,1,0,1,0,2,0,3,0,1,

%T 1,1,0,1,0,2,0,2,0,1,0,1,0,3,0,1,0,1,0,3,1,2,0,1,0,1,0,1,0,3,1,2,0,1,

%U 0,1,0,2,0,1,1,1,0,2,0,3,0,1,0,1,1,1,0,2,0,3,0,1,0,1,1,3,0,2,0,2,0,2,0,2,1

%N a(1) = 0, and for n > 1, a(n) = [A122111(n) == 3 (mod 4)] + a(A253553(n)).

%C Positions for the first occurrence of each n, for n >= 0, are: 1, 4, 16, 32, 144, 512, 2048, 6912, 20736, 62208, ...

%H Antti Karttunen, <a href="/A336121/b336121.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 0, and for n > 1, a(n) = [A336124(n) == 3] + a(A253553(n)).

%F a(n) = A000120(A336120(n)).

%F a(n) = A292377(A122111(n)).

%F a(n) = A001222(n) - A336123(n).

%o (PARI)

%o A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));

%o A336121(n) = if(1==n,0,(3==A336124(n))+A336121(A253553(n)));

%Y Cf. A000120, A001222, A122111, A253553, A292377, A292383, A336120, A336123, A336124.

%Y Cf. A336119 (positions of zeros).

%K nonn

%O 1,16

%A _Antti Karttunen_, Jul 17 2020