A288636 Height of power-tower factorization of n. Row lengths of A278028.

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

Offset: 1

Author

Gus Wiseman, Jun 12 2017

Keywords

• nonn

Comments

After a(1)=0 this sequence has many terms equal to A089723. It first differs at a(64)=2, A089723(64)=4.

First positions of a(n) = {0, 1, 2, 3, 4} are n = {1, 2, 4, 16, 65536}. - Michael De Vlieger, Nov 24 2017

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..65536

Crossrefs

Cf. A007916, A089723, A164337, A277562, A277564, A278028.

Programs

Mathematica

a[n_] := If[n == 1, 0, 1+a[GCD @@ FactorInteger[n][[All, 2]]]];
Array[a,100]