A304328 a(n) = n/(largest perfect power divisor of n).

1, 2, 3, 1, 5, 6, 7, 1, 1, 10, 11, 3, 13, 14, 15, 1, 17, 2, 19, 5, 21, 22, 23, 3, 1, 26, 1, 7, 29, 30, 31, 1, 33, 34, 35, 1, 37, 38, 39, 5, 41, 42, 43, 11, 5, 46, 47, 3, 1, 2, 51, 13, 53, 2, 55, 7, 57, 58, 59, 15, 61, 62, 7, 1, 65, 66, 67, 17, 69, 70, 71, 2

Offset: 1

Author

Gus Wiseman, May 10 2018

Keywords

• nonn

Comments

Not all terms are squarefree numbers; for example, a(500) = 4.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000961, A001055, A001222, A001597, A001694, A005117, A007716, A007916, A052485, A052486, A059404, A066636, A091050, A160400, A203025, A294068, A303707, A304327, A304339.

Programs

Mathematica

Table[n/Last[Select[Divisors[n],#===1||GCD@@FactorInteger[#][[All,2]]>1&]],{n,100}]

PARI

a(n)={my(m=1); fordiv(n, d, if(ispower(d), m=max(m,d))); n/m} \\ Andrew Howroyd, Aug 26 2018

Formula

a(n) * A203025(n) = n.