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A325275
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Heinz number of the omega-sequence of n!.
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7
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1, 1, 2, 18, 126, 990, 850, 11970, 19530, 25830, 4606, 73458, 92862, 116298, 43134, 229086, 275418, 366894, 440946, 515394, 568062, 613206, 769158, 963378, 1060254, 1135602, 6108570, 6431490, 6915870, 8923590, 9398610, 10191870, 11352510, 3139866, 16458210
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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MATHEMATICA
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omseq[n_Integer]:=If[n<=1, {}, Total/@NestWhileList[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Total[#]>1&]];
Table[Times@@Prime/@omseq[n!], {n, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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