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A008477
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If n = Product (p_j^k_j) then a(n) = Product (k_j^p_j).
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8
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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; internal format)
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OFFSET
| 1,4
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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]
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REFERENCES
| M. Farrokhi, Problem 11315, Amer. Math. Monthly, 116 (2009), 470. - from N. J. A. Sloane, Apr 25 2009
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| Multiplicative with a(p^e) = e^p. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MAPLE
| A008477 := proc(n) local e, j; e := ifactors(n)[2]:
mul (e[j][2]^e[j][1], j=1..nops(e)) end:
seq (A008477(n), n=1..60);
# - Peter Luschny, Jan 17 2010
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MATHEMATICA
| Prepend[ Array[ Times @@ Map[ Power @@ RotateLeft[ #1, 1 ]&, FactorInteger[ # ] ]&, 100, 2 ], 1 ]
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PROG
| (Haskell)
a008477 n = product $ zipWith (^) (a124010_row n) (a027748_row n)
-- Reinhard Zumkeller, Feb 17 2012
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CROSSREFS
| Cf. A027748, A124010.
Sequence in context: A057521 A084885 A112538 * A184729 A127707 A113196
Adjacent sequences: A008474 A008475 A008476 * A008478 A008479 A008480
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KEYWORD
| nonn,mult,changed
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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