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A325274 Sum of the omega-sequence of n!. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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), with sum 13.

LINKS

Table of n, a(n) for n=0..59.

MATHEMATICA

omseq[n_Integer]:=If[n<=1, {}, Total/@NestWhileList[Sort[Length/@Split[#]]&, Sort[Last/@FactorInteger[n]], Total[#]>1&]];

Table[Total[omseq[n!]], {n, 0, 100}]

CROSSREFS

a(n) = A056239(A325275(n)).

Cf. A000142, A006939, A303555, A323023, A325238, A325272, A325273, A325276, A325277.

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).

Sequence in context: A130333 A304868 A080579 * A303264 A165971 A160522

Adjacent sequences:  A325271 A325272 A325273 * A325275 A325276 A325277

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 18 2019

STATUS

approved

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Last modified October 16 01:48 EDT 2019. Contains 328038 sequences. (Running on oeis4.)