%I #23 Sep 15 2023 06:18:52
%S 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,
%T 26,27,196,29,30,31,32,33,34,35,36,37,38,39,1000,41,42,43,484,225,46,
%U 47,1296,49,100,51,676,53,216,55,2744,57,58,59
%N Smallest power of a squarefree number that is a multiple of n.
%H Reinhard Zumkeller, <a href="/A066638/b066638.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = rad(n)^mpe(n), (rad=A007947, mpe=A051903).
%F a(n) = A066636(n) * n. - _Amiram Eldar_, Sep 15 2023
%e a(40)=10^3 > 40 > 10=rad(40).
%t 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 *)
%o (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
%o (Haskell)
%o a066638 n = a007947 n ^ a051903 n -- _Reinhard Zumkeller_, Jun 17 2015
%Y Cf. A005117, A066636.
%Y Cf. A007947, A051903.
%K nonn,nice
%O 1,2
%A _Reinhard Zumkeller_, Jan 09 2002