A322989 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,12

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

FORMULA

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

PROG

(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);

CROSSREFS

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

Cf. also A322823.

Sequence in context: A295859 A180160 A101661 * A322823 A334872 A263844

Adjacent sequences: A322986 A322987 A322988 * A322990 A322991 A322992

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 01 2019

STATUS

approved