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 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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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). 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

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Last modified January 27 05:36 EST 2021. Contains 340455 sequences. (Running on oeis4.)