A304339 Fixed point of f starting with n, where f(x) = x/(largest perfect power divisor of x).

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

1,2

Comments

All terms are squarefree numbers. First differs from A304328 at a(500) = 1, A304328(500) = 4.

Links

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

Example

f maps 500 -> 4 -> 1 -> 1, so a(500) = 1.

Mathematica

radQ[n_]:=And[n>1, GCD@@FactorInteger[n][[All, 2]]===1];
op[n_]:=n/Last[Select[Divisors[n], !radQ[#]&]];
Table[FixedPoint[op, n], {n, 200}]

Prog

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

Crossrefs

Cf. A000961, A001597, A001694, A005117, A007916, A052485, A052486, A059404, A091050, A160400, A203025, A294068, A303707, A304327, A304328.

Sequence in context: A362248 A055231 A304328 * A160400 A325978 A326049

Adjacent sequences: A304336 A304337 A304338 * A304340 A304341 A304342

Keyword

nonn

Author

Gus Wiseman, May 11 2018

Status

approved