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A066638
Smallest power of a squarefree number that is a multiple of n.
10
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 36, 13, 14, 15, 16, 17, 36, 19, 100, 21, 22, 23, 216, 25, 26, 27, 196, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 1000, 41, 42, 43, 484, 225, 46, 47, 1296, 49, 100, 51, 676, 53, 216, 55, 2744, 57, 58, 59
OFFSET
1,2
LINKS
FORMULA
a(n) = rad(n)^mpe(n), (rad=A007947, mpe=A051903).
a(n) = A066636(n) * n. - Amiram Eldar, Sep 15 2023
EXAMPLE
a(40)=10^3 > 40 > 10=rad(40).
MATHEMATICA
rad[n_] := Times @@ First /@ FactorInteger[n]; mpe[n_] := Max @@ Last /@ FactorInteger[n]; mpe[1] = 0; a[n_] := rad[n]^mpe[n]; Table[a[n], {n, 1, 59}] (* Jean-François Alcover, Mar 27 2013 *)
PROG
(PARI) a(n)=if(n==1, return(1)); my(f=factor(n)); prod(i=1, #f~, f[i, 1])^ vecmax(f[, 2]) \\ Charles R Greathouse IV, Aug 21 2013
(Haskell)
a066638 n = a007947 n ^ a051903 n -- Reinhard Zumkeller, Jun 17 2015
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Jan 09 2002
STATUS
approved