A323014 - OEIS

A323014

a(1) = 0; a(prime) = 1; otherwise a(n) = 1 + a(A181819(n)).

0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 2, 3, 3, 3, 3, 1, 3, 3, 4, 1, 3, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 5, 1, 3, 4, 2, 3, 3, 1, 4, 3, 3, 1, 4, 1, 3, 4, 4, 3, 3, 1, 4, 2, 3, 1, 5, 3, 3, 3, 4, 1, 5, 3, 4, 3, 3, 3, 4, 1, 4, 4, 3, 1, 3, 1, 4, 3

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

OFFSET

1,4

COMMENTS

Except for n = 2, same as A182850. Unlike A182850, the terms of this sequence depend only on the prime signature (A101296, A118914) of the index.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

FORMULA

For all n >= 1, a(n) = a(A046523(n)). [See comment] - Antti Karttunen, Jun 10 2022

MATHEMATICA

dep[n_]:=If[n==1, 0, If[PrimeQ[n], 1, 1+dep[Times@@Prime/@Last/@FactorInteger[n]]]];