

A325410


Smallest k such that the adjusted frequency depth of k! is n > 2.


2




OFFSET

3,1


COMMENTS

If infinite terms were allowed, we would have a(0) = 1, a(1) = 2, a(2) = infinity. It is possible this sequence is finite, or that there are additional gaps.
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.


LINKS

Table of n, a(n) for n=3..10.


EXAMPLE

Column n is the sequence of images under A181819 starting with a(n)!:
6 24 120 5040 403291461126605635584000000
4 10 20 84 11264760
3 4 6 12 240
3 4 6 28
3 4 6
3 4
3


MATHEMATICA

fdadj[n_Integer]:=If[n==1, 0, Length[NestWhileList[Times@@Prime/@Last/@FactorInteger[#]&, n, !PrimeQ[#]&]]];
dat=Table[fdadj[n!], {n, 1000}];
Table[Position[dat, k][[1, 1]], {k, 3, Max@@dat}]


CROSSREFS

a(n) is the first position of n in A325272.
Cf. A000142, A022559, A181819, A181821, A323023, A325238, A325273, A325274, A325275, A325276, A325277.
Omegasequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (secondtolast omega), A182850 or A323014 (frequency depth), A325248 (Heinz number), A325249 (sum).
Sequence in context: A216433 A101761 A035359 * A269719 A214626 A143593
Adjacent sequences: A325407 A325408 A325409 * A325411 A325412 A325413


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Apr 24 2019


STATUS

approved



