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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
Brahim Mittou, New properties of an arithmetic function, Mathematica Montisnigri, Vol LIII (2022).
Eric Weisstein's World of Mathematics, Cubefree.
FORMULA
Multiplicative with a(p^e) = p^(2 - e mod 2), p prime, e>0.
Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/30) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 0.4296463408... . - Amiram Eldar, Oct 28 2022
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
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(2 - f[i, 2]%2)); } \\ Amiram Eldar, Oct 28 2022
CROSSREFS
Sequence in context: A043267 A167514 A091733 * A365296 A097449 A104415
KEYWORD
nonn,nice,mult
AUTHOR
Reinhard Zumkeller, Feb 01 2002
STATUS
approved

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Last modified April 15 05:10 EDT 2024. Contains 371667 sequences. (Running on oeis4.)