A322989 If n is a power of a prime, then a(n) = 0, otherwise a(n) = 1 + a(A322990(n)).

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 0, 1, 0, 3, 2, 1, 0, 2, 0, 1, 0, 3, 0, 2, 0, 0, 2, 1, 4, 3, 0, 1, 2, 4, 0, 2, 0, 3, 4, 1, 0, 2, 0, 1, 2, 3, 0, 1, 4, 5, 2, 1, 0, 3, 0, 1, 5, 0, 4, 2, 0, 3, 2, 3, 0, 6, 0, 1, 2, 3, 5, 2, 0, 4, 0, 1, 0, 3, 4, 1, 2, 6, 0, 3, 5, 3, 2, 1, 4, 2, 0, 1, 7, 3, 0, 2, 0, 6, 4

Offset: 1

Author

Antti Karttunen, Jan 01 2019

Keywords

• nonn

Comments

For n > 1, a(n) gives the number of edges needed from n to the leftmost branch (where the terms of A000961 are located) in the binary tree illustrated in A289272.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000961, A001221, A010055, A289272, A322990.

Cf. also A322823.

Programs

PARI

A289271(n) = { my(v=0,i=0,x=1); for(d=2,oo,if(n==1, return(v)); if(1==gcd(x,d)&&1==omega(d), if(!(n%d)&&1==gcd(d,n/d), v += 2^i; n /= d; x *= d); i++)); }; \\ After Rémy Sigrist's program for A289271.
A289272(n) = { my(m=1, pp=1); while(n>0, pp++; while(!isprimepower(pp)||(gcd(pp,m)>1), pp++); if(n%2, m *= pp); n >>=1); (m); };
A322989(n) = if((1==n)||isprimepower(n),0,1+A322989(A322990(n)));
A322990(n) = A289272(A289271(n)>>1);

Formula

If A001221(n) <= 1 [when n is in A000961], then a(n) = 0, otherwise a(n) = 1 + a(A322990(n)).