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 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. 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(1) = 0 by convention. LINKS 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

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)