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 A008477 If n = Product (p_j^k_j) then a(n) = Product (k_j^p_j). 22
 1, 1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 4, 1, 1, 1, 16, 1, 8, 1, 4, 1, 1, 1, 9, 32, 1, 27, 4, 1, 1, 1, 25, 1, 1, 1, 32, 1, 1, 1, 9, 1, 1, 1, 4, 8, 1, 1, 16, 128, 32, 1, 4, 1, 27, 1, 9, 1, 1, 1, 4, 1, 1, 8, 36, 1, 1, 1, 4, 1, 1, 1, 72, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For any n, the sequence n, a(n), a(a(n)), a(a(a(n))), ... is eventually periodic with period <= 2 [Farrokhi]. - N. J. A. Sloane, Apr 25 2009 a(A005117(n)) = 1; a(A013929(n)) > 1; A010052(a(A122132(n))) = 1. - Reinhard Zumkeller, Feb 17 2012 From Bernard Schott, Mar 26 2021: (Start) The study of some properties of this sequence was proposed in the 1st problem of Concours Général in 2012 in France (see links). Terms are precisely the powerful numbers in A001694. If m is a term, there is a term q such that a(q) = m. a(a(n)) <= n (see examples). (End) LINKS M. F. Hasler, Table of n, a(n) for n = 1..10000 Annales Concours Général, Sujet Concours Général 2012 (in French, problems). Annales Concours Général, Corrigé Concours Général 2012 (in French, solutions). M. Farrokhi, The Prime Exponentiation of an Integer: Problem 11315, Amer. Math. Monthly, 116 (2009), 470. - from N. J. A. Sloane, Apr 25 2009 FORMULA Multiplicative with a(p^e) = e^p. - David W. Wilson, Aug 01 2001 EXAMPLE For n = 24 = 2^3*3^1, a(24) = 3^2*1^3 = 9, so a(9) = 2^3 = 8 and a(a(24)) = 8 < 24. For n = 243 = 3^5, a(243) = 5^3 = 125, so a(125) = 3^5 = 243 and a(a(243)) = 243. MAPLE A008477 := proc(n) local e, j; e := ifactors(n): mul (e[j]^e[j], j=1..nops(e)) end: seq (A008477(n), n=1..60); # Peter Luschny, Jan 17 2010 MATHEMATICA Prepend[ Array[ Times @@ Map[ Power @@ RotateLeft[ #1, 1 ]&, FactorInteger[ # ] ]&, 100, 2 ], 1 ] Table[Times@@(First[#]^Last[#]&/@Transpose[Reverse[ Transpose[ FactorInteger[ n]]]]), {n, 80}] (* Harvey P. Dale, Jul 22 2014 *) PROG (Haskell) a008477 n = product \$ zipWith (^) (a124010_row n) (a027748_row n) -- Reinhard Zumkeller, Feb 17 2012 (PARI) A008477(n)=factorback(factor(n)*[0, 1; 1, 0])  \\ M. F. Hasler, May 20 2012 CROSSREFS Cf. A001694, A027748, A124010. Cf. A005117, A013929, A010052, A062307, A122132, A342551. Cf. A008478 (fixed points). Sequence in context: A057521 A084885 A112538 * A303278 A222639 A184729 Adjacent sequences:  A008474 A008475 A008476 * A008478 A008479 A008480 KEYWORD nonn,mult AUTHOR STATUS approved

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Last modified October 2 12:49 EDT 2022. Contains 357205 sequences. (Running on oeis4.)