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%I #9 Apr 25 2019 13:30:36
%S 1,2,0,3,4,5,7,26,65,942,24147
%N Smallest k such that the adjusted frequency depth of k! is n, and 0 if there is no such k.
%C 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.
%C Conjecture: this sequence has infinitely many nonzero terms.
%e Column n is the sequence of images under A181819 starting with a(n)!:
%e - 2 - 6 24 120 5040 403291461126605635584000000
%e 4 10 20 84 11264760
%e 3 4 6 12 240
%e 3 4 6 28
%e 3 4 6
%e 3 4
%e 3
%Y Essentially the same as A325410.
%Y a(n) is zero or the first position of n in A325272.
%Y Cf. A000142, A323023, A325238, A325273, A325274, A325275, A325276, A325277, A325416.
%Y 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), A325249 (sum).
%K nonn,more
%O 0,2
%A _Gus Wiseman_, Apr 25 2019