OFFSET
0,2
COMMENTS
The adjusted frequency depth of a positive integer n is 0 if n = 1, and otherwise it is 1 plus the number of times one must apply A181819 to reach a prime number, where A181819(k = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of k. For example, 180 has adjusted frequency depth 5 because we have: 180 -> 18 -> 6 -> 4 -> 3.
Differs from A182857 in having 2 instead of 3.
MATHEMATICA
nn=10000;
fd[n_]:=Switch[n, 1, 0, _?PrimeQ, 1, _, 1+fd[Times@@Prime/@Last/@FactorInteger[n]]];
fds=fd/@Range[nn];
Sort[Table[Position[fds, x][[1, 1]], {x, Union[fds]}]]
CROSSREFS
A subsequence of A325238.
Cf. A011784, A056239, A112798, A118914, A181819, A181821, A182857, A225485, A323023, A325258, A325272, A325277, A325278, A325280.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 17 2019
STATUS
approved