A336123 a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A122111(n) == 1 (mod 4)] + a(A253553(n)).

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 4, 1, 1, 3, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 1, 2, 2

Offset: 1

Author

Antti Karttunen, Jul 17 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000120, A000244, A001222, A122111, A292375, A336121, A336124, A336125.

Programs

PARI

\\ Uses also code given in A336124:
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));
A336123(n) = if(n<=2,n-1,(1==A336124(n))+A336123(A253553(n)));

Formula

a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A336124(n) == 1] + a(A253553(n)).

a(n) = A000120(A336125(n)).

For n > 1, a(n) = A292375(A122111(n)).

a(n) = A001222(n) - A336121(n).

For all n >= 0, a(3^n) = n.