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.

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

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 * A345354 A238951 A071466

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