A066638 Smallest power of a squarefree number that is a multiple of n.

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

Author

Reinhard Zumkeller, Jan 09 2002

Keywords

• nonn
• nice

Examples

			a(40)=10^3 > 40 > 10=rad(40).
		

Links

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

Crossrefs

Cf. A005117, A066636.

Cf. A007947, A051903.

Programs

Haskell

a066638 n = a007947 n ^ a051903 n  -- Reinhard Zumkeller, Jun 17 2015

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 *)

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

Formula

a(n) = rad(n)^mpe(n), (rad=A007947, mpe=A051903).

a(n) = A066636(n) * n. - Amiram Eldar, Sep 15 2023