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 A325266 #6 Apr 17 2019 19:08:58
%S A325266 1,2,3,4,5,7,9,11,13,17,19,23,24,25,29,30,31,37,40,41,42,43,47,49,53,
%T A325266 54,56,59,61,66,67,70,71,73,78,79,83,88,89,97,101,102,103,104,105,107,
%U A325266 109,110,113,114,120,121,127,130,131,135,136,137,138,139,149
%N A325266 Numbers whose adjusted frequency depth equals their number of prime factors counted with multiplicity.
%C A325266 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(n = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of n. For example, 180 has adjusted frequency depth 5 because we have: 180 -> 18 -> 6 -> 4 -> 3.
%C A325266 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose adjusted frequency depth is equal to their length. The enumeration of these partitions by sum is given by A325246.
%e A325266 The sequence of terms together with their prime indices and their omega-sequences (see A323023) begins:
%e A325266 2: {1} (1)
%e A325266 3: {2} (1)
%e A325266 4: {1,1} (2,1)
%e A325266 5: {3} (1)
%e A325266 7: {4} (1)
%e A325266 9: {2,2} (2,1)
%e A325266 11: {5} (1)
%e A325266 13: {6} (1)
%e A325266 17: {7} (1)
%e A325266 19: {8} (1)
%e A325266 23: {9} (1)
%e A325266 24: {1,1,1,2} (4,2,2,1)
%e A325266 25: {3,3} (2,1)
%e A325266 29: {10} (1)
%e A325266 30: {1,2,3} (3,3,1)
%e A325266 31: {11} (1)
%e A325266 37: {12} (1)
%e A325266 40: {1,1,1,3} (4,2,2,1)
%e A325266 41: {13} (1)
%e A325266 42: {1,2,4} (3,3,1)
%t A325266 fdadj[n_Integer]:=If[n==1,0,Length[NestWhileList[Times@@Prime/@Last/@FactorInteger[#]&,n,!PrimeQ[#]&]]];
%t A325266 Select[Range[100],fdadj[#]==PrimeOmega[#]&]
%Y A325266 Cf. A056239, A112798, A118914, A181819, A225485, A323023, A325246, A325258, A325277, A325278, A325281, A325283.
%Y A325266 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).
%K A325266 nonn
%O A325266 1,2
%A A325266 _Gus Wiseman_, Apr 17 2019