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 A305829 Factor n into distinct Fermi-Dirac primes (A050376), normalize by replacing every instance of the k-th Fermi-Dirac prime with k, then multiply everything together. 12
 1, 1, 2, 3, 4, 2, 5, 3, 6, 4, 7, 6, 8, 5, 8, 9, 10, 6, 11, 12, 10, 7, 12, 6, 13, 8, 12, 15, 14, 8, 15, 9, 14, 10, 20, 18, 16, 11, 16, 12, 17, 10, 18, 21, 24, 12, 19, 18, 20, 13, 20, 24, 21, 12, 28, 15, 22, 14, 22, 24, 23, 15, 30, 27, 32, 14, 24, 30, 24, 20, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive integer n has a unique factorization of the form n = f(s_1)*...*f(s_k) where the s_i are strictly increasing positive integers. Then a(n) = s_1 * ... * s_k. Multiplicative because for coprime m and n the Fermi-Dirac factorizations of m and n are disjoint and their union is the Fermi-Dirac factorization of m * n. - Andrew Howroyd, Aug 02 2018 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 Gus Wiseman, Tree of x -> a(x) for n = 1...75 MATHEMATICA nn=100; FDfactor[n_]:=If[n===1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]]; FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList]; Table[Times@@(FDfactor[n]/.FDrules), {n, nn}] PROG (PARI) \\ here isfd is membership test for A050376. isfd(n)={my(e=isprimepower(n)); e && e == 1<

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Last modified October 18 05:26 EDT 2019. Contains 328146 sequences. (Running on oeis4.)