

A307734


Smallest k such that the adjusted frequency depth of k! is n, and 0 if there is no such k.


1



1, 2, 0, 3, 4, 5, 7, 26, 65, 942, 24147
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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.
Conjecture: this sequence has infinitely many nonzero terms.


LINKS

Table of n, a(n) for n=0..10.


EXAMPLE

Column n is the sequence of images under A181819 starting with a(n)!:
 2  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


CROSSREFS

Essentially the same as A325410.
a(n) is zero or the first position of n in A325272.
Cf. A000142, A323023, A325238, A325273, A325274, A325275, A325276, A325277, A325416.
Omegasequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (secondtolast omega), A182850 or A323014 (length/frequency depth), A325248 (Heinz number), A325249 (sum).
Sequence in context: A173517 A109921 A139637 * A243202 A257136 A258871
Adjacent sequences: A307731 A307732 A307733 * A307735 A307736 A307737


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Apr 25 2019


STATUS

approved



