login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304455 Number of steps in the reduction to a multiset of size 1 of the multiset of prime factors of n, obtained by repeatedly taking the multiset of multiplicities. 9
0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 1, 0, 3, 0, 3, 2, 2, 0, 3, 1, 2, 1, 3, 0, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 0, 3, 3, 2, 0, 3, 1, 3, 2, 3, 0, 3, 2, 3, 2, 2, 0, 4, 0, 2, 3, 1, 2, 2, 0, 3, 2, 2, 0, 3, 0, 2, 3, 3, 2, 2, 0, 3, 1, 2, 0, 4, 2, 2, 2, 3, 0, 4, 2, 3, 2, 2, 2, 3, 0, 3, 3, 2, 0, 2, 0, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

FORMULA

For n > 2, a(n) = A182850(n) - 1.

a(prime(n)) = 0.

a(A246547(n)) = 1.

EXAMPLE

The a(2520) = 5 steps are {2,2,2,3,3,5,7} -> {1,1,2,3} -> {1,1,2} -> {1,2} -> {1,1} -> {2}.

MATHEMATICA

Table[Length[Select[FixedPointList[Sort[Length/@Split[#]]&, If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[p, {k}]]]]], Length[#]>1&]], {n, 100}]

PROG

(PARI)

A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));

A304455(n) = if(n<=2, 0, n=A181819(n); if(2==n, 0, 1+A304455(n))); \\ Antti Karttunen, Dec 06 2018

CROSSREFS

Cf. A000961, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A130091, A181819, A182850, A182853, A182857, A303945, A304464, A304465, A320118.

Sequence in context: A185279 A088432 A329747 * A238951 A071466 A155041

Adjacent sequences:  A304452 A304453 A304454 * A304456 A304457 A304458

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 12 2018

EXTENSIONS

More terms from Antti Karttunen, Dec 06 2018

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 August 13 00:27 EDT 2020. Contains 336441 sequences. (Running on oeis4.)