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 A325410 Smallest k such that the adjusted frequency depth of k! is n > 2. 2
 3, 4, 5, 7, 26, 65, 942, 24147 (list; graph; refs; listen; history; text; internal format)
 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 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. Omega-sequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (second-to-last 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

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)