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A008477 If n = Product (p_j^k_j) then a(n) = Product (k_j^p_j). 11
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]

REFERENCES

M. Farrokhi, Problem 11315, Amer. Math. Monthly, 116 (2009), 470. - from N. J. A. Sloane, Apr 25 2009

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = e^p. - David W. Wilson, Aug 01, 2001.

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

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. A027748, A124010.

Sequence in context: A057521 A084885 A112538 * A222639 A184729 A127707

Adjacent sequences:  A008474 A008475 A008476 * A008478 A008479 A008480

KEYWORD

nonn,mult

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 28 15:38 EDT 2017. Contains 284243 sequences.