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

1,2

Links

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

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

Cf. A005117, A066636.

Cf. A007947, A051903.

Sequence in context: A300819 A161949 A004851 * A285769 A219209 A223474

Adjacent sequences: A066635 A066636 A066637 * A066639 A066640 A066641

Keyword

nonn,nice

Author

Reinhard Zumkeller, Jan 09 2002

Status

approved