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A325274
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Sum of the omega-sequence of n!.
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7
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0, 0, 1, 5, 9, 13, 14, 20, 23, 25, 24, 30, 33, 35, 35, 40, 44, 46, 49, 51, 54, 56, 59, 61, 65, 67, 72, 75, 78, 80, 83, 85, 90, 90, 95, 97, 101, 103, 105, 106, 110, 112, 115, 117, 122, 125, 127, 129, 134, 136, 139, 140, 143, 145, 149, 153, 157, 159, 160, 162
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OFFSET
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0,4
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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), with sum 13.
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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[Total[omseq[n!]], {n, 0, 100}]
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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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