The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304455

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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.
(history; published version)

#17 by Susanna Cuyler at Thu Dec 06 16:33:30 EST 2018

STATUS

proposed

approved

#16 by Antti Karttunen at Thu Dec 06 13:53:28 EST 2018

STATUS

editing

proposed

#15 by Antti Karttunen at Thu Dec 06 10:18:08 EST 2018

LINKS

<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

#14 by Antti Karttunen at Thu Dec 06 10:16:28 EST 2018

LINKS

Antti Karttunen, <a href="/A304455/b304455.txt">Table of n, a(n) for n = 1..20000</a>

#13 by Antti Karttunen at Thu Dec 06 10:12:35 EST 2018

FORMULA

a(A000961A246547(n)) = 1.

#12 by Antti Karttunen at Thu Dec 06 10:10:24 EST 2018

LINKS

Antti Karttunen, <a href="/A304455/a304455.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

FORMULA

a(prime(n > 1)) = 0.

CROSSREFS

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

#11 by Antti Karttunen at Thu Dec 06 10:06:23 EST 2018

DATA

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

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

EXTENSIONS

More terms from Antti Karttunen, Dec 06 2018

STATUS

approved

editing

#10 by Susanna Cuyler at Mon May 14 20:21:39 EDT 2018

STATUS

proposed

approved

#9 by Gus Wiseman at Sun May 13 09:41:31 EDT 2018

STATUS

editing

proposed

#8 by Gus Wiseman at Sun May 13 09:40:16 EDT 2018

EXAMPLE

The a(2520) = 5 steps are {1,1,1,2,2,2,3,3,45,7} -> {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[PrimePi[p], , {k}]]]]], Length[#]>1&]], {n, 100}]