A328479 a(n) = n/A328478(n), where A328478(n) is obtained by repeatedly dividing n by the largest primorial that divides it until a fixed point is reached.

1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 16, 1, 6, 1, 4, 1, 2, 1, 24, 1, 2, 1, 4, 1, 30, 1, 32, 1, 2, 1, 36, 1, 2, 1, 8, 1, 6, 1, 4, 1, 2, 1, 48, 1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 60, 1, 2, 1, 64, 1, 6, 1, 4, 1, 2, 1, 72, 1, 2, 1, 4, 1, 6, 1, 16, 1, 2, 1, 12, 1, 2, 1, 8, 1, 30, 1, 4, 1, 2, 1, 96, 1, 2, 1, 4, 1, 6, 1, 8, 1

Offset: 1

Author

Antti Karttunen, Oct 19 2019

Keywords

• nonn

Comments

a(n) is the largest term in A025487 that divides n evenly. - Hal M. Switkay, May 04 2021

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A053589, A111701, A328478.

Programs

Mathematica

A111701[n_] := A111701[n] = Block[{m = n, k = 1}, While[IntegerQ[m/Prime[k]], m = m/Prime[k]; k++]; m];
A328478[n_] := If[A111701[n] == n, n, A328478[A111701[n]]];
A328479[n_] := n/A328478[n];
Array[A328479, 105] (* Jean-François Alcover, Jan 11 2022, after Robert G. Wilson v in A111701 *)

PARI

A111701(n) = forprime(p=2, , if(n%p, return(n), n /= p));
A328478(n) = { my(u=A111701(n)); if(u==n, return(n), return(A328478(u))); };
A328479(n) = (n/A328478(n));

Formula

a(n) = n / A328478(n).