A304464 Start with the normalized multiset of prime factors of n > 1. Given a multiset, take the multiset of its multiplicities. Repeat this until a multiset of size 1 is obtained. a(n) is the unique element of this multiset.

0, 1, 2, 2, 3, 2, 4, 3, 2, 2, 5, 2, 6, 2, 2, 4, 7, 2, 8, 2, 2, 2, 9, 2, 2, 2, 3, 2, 10, 3, 11, 5, 2, 2, 2, 2, 12, 2, 2, 2, 13, 3, 14, 2, 2, 2, 15, 2, 2, 2, 2, 2, 16, 2, 2, 2, 2, 2, 17, 2, 18, 2, 2, 6, 2, 3, 19, 2, 2, 3, 20, 2, 21, 2, 2, 2, 2, 3, 22, 2, 4, 2, 23

Offset

1,3

Comments

a(1) = 0 by convention.

Links

Table of n, a(n) for n=1..83.

Formula

a(prime(n)) = n.

a(p^n) = n where p is any prime number and n > 1.

a(product of n > 1 distinct primes) = n.

Example

Starting with the normalized multiset of prime factors of 360, we obtain {1,1,1,2,2,3} -> {1,2,3} -> {1,1,1} -> {3}, so a(360) = 3.

Mathematica

Table[If[n===1, 0, NestWhile[Sort[Length/@Split[#]]&, If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]], Length[#]>1&]//First], {n, 100}]

Crossrefs

Cf. A000005, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A181819, A182850, A182857, A275870, A296150, A303945, A304465.

Sequence in context: A175501 A144370 A239514 * A087050 A341285 A263323

Adjacent sequences: A304461 A304462 A304463 * A304465 A304466 A304467

Keyword

nonn

Author

Gus Wiseman, May 13 2018

Status

approved