OFFSET
0,3
COMMENTS
We define the omega-sequence of n (row n of A323023) to have length A323014(n) = adjusted frequency depth of n, and the k-th term is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of red = A181819, defined by red(n = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of n. For example, we have 180 -> 18 -> 6 -> 4 -> 3, so the omega-sequence of 180 is (5,3,2,2,1).
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
MATHEMATICA
omseq[n_Integer]:=If[n<=1, {}, Total/@NestWhileList[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Total[#]>1&]];
Table[Times@@Prime/@omseq[n!], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 18 2019
STATUS
approved