login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325275 Heinz number of the omega-sequence of n!. 7
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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=0..34.

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

A001222(a(n)) = A325272.

A055396(a(n)/2) = A325273.

A056239(a(n)) = A325274.

Row n of A325276 is row a(n) of A112798.

Cf. A000142, A006939, A056239, A112798, A303555, A323023, A325238, 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: A052653 A289830 A060589 * A277661 A064447 A043022

Adjacent sequences:  A325272 A325273 A325274 * A325276 A325277 A325278

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 18 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 07:58 EDT 2019. Contains 327168 sequences. (Running on oeis4.)