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A066990 In canonical prime factorization of n replace even exponents with 2 and odd exponents with 1. 2
1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 15, 4, 17, 18, 19, 20, 21, 22, 23, 6, 25, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 36, 37, 38, 39, 10, 41, 42, 43, 44, 45, 46, 47, 12, 49, 50, 51, 52, 53, 6, 55, 14, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = n for cubefree numbers (A004709), whereas a(n) <> n for cube-full numbers (A046099).

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cubefree

FORMULA

Multiplicative with a(p^e) = p^(2 - e mod 2), p prime, e>0.

MATHEMATICA

fx[{a_, b_}]:={a, If[EvenQ[b], 2, 1]}; Table[Times@@(#[[1]]^#[[2]]&/@(fx/@ FactorInteger[n])), {n, 70}] (* Harvey P. Dale, Jan 01 2012 *)

PROG

(Haskell)

a066990 n = product $ zipWith (^)

           (a027748_row n) (map ((2 -) . (`mod` 2)) $ a124010_row n)

-- Reinhard Zumkeller, Dec 02 2012

CROSSREFS

Sequence in context: A043267 A167514 A091733 * A097449 A104415 A071074

Adjacent sequences:  A066987 A066988 A066989 * A066991 A066992 A066993

KEYWORD

nonn,nice,mult

AUTHOR

Reinhard Zumkeller, Feb 01 2002

STATUS

approved

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Last modified May 16 23:46 EDT 2021. Contains 343957 sequences. (Running on oeis4.)