A325278 Smallest number with adjusted frequency depth n.

1, 2, 4, 6, 12, 60, 2520, 1286485200, 35933692027611398678865941374040400000

Offset: 0

Author

Gus Wiseman, Apr 17 2019

Keywords

• nonn

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.

Crossrefs

A subsequence of A325238.

Cf. A011784, A056239, A112798, A118914, A181819, A181821, A182857, A225485, A323023, A325258, A325272, A325277, A325278, A325280.

Omega-sequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (second-to-last omega), A182850 or A323014 (length/frequency depth), A325248 (Heinz number).

Programs

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]}]]