This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307734 #9 Apr 25 2019 13:30:36 %S A307734 1,2,0,3,4,5,7,26,65,942,24147 %N A307734 Smallest k such that the adjusted frequency depth of k! is n, and 0 if there is no such k. %C A307734 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 A307734 Conjecture: this sequence has infinitely many nonzero terms. %e A307734 Column n is the sequence of images under A181819 starting with a(n)!: %e A307734 - 2 - 6 24 120 5040 403291461126605635584000000 %e A307734 4 10 20 84 11264760 %e A307734 3 4 6 12 240 %e A307734 3 4 6 28 %e A307734 3 4 6 %e A307734 3 4 %e A307734 3 %Y A307734 Essentially the same as A325410. %Y A307734 a(n) is zero or the first position of n in A325272. %Y A307734 Cf. A000142, A323023, A325238, A325273, A325274, A325275, A325276, A325277, A325416. %Y A307734 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 A307734 nonn,more %O A307734 0,2 %A A307734 _Gus Wiseman_, Apr 25 2019