A328478 Divide n by the largest primorial that divides it and repeat until a fixed point is reached; a(n) is the fixed point.

1, 1, 3, 1, 5, 1, 7, 1, 9, 5, 11, 1, 13, 7, 15, 1, 17, 3, 19, 5, 21, 11, 23, 1, 25, 13, 27, 7, 29, 1, 31, 1, 33, 17, 35, 1, 37, 19, 39, 5, 41, 7, 43, 11, 45, 23, 47, 1, 49, 25, 51, 13, 53, 9, 55, 7, 57, 29, 59, 1, 61, 31, 63, 1, 65, 11, 67, 17, 69, 35, 71, 1, 73, 37, 75, 19, 77, 13, 79, 5, 81, 41, 83, 7, 85, 43, 87, 11, 89

Offset: 1

Author

Antti Karttunen, Oct 19 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A007814 (gives the number of iterations to reach a fixed point), A025487 (indices of 1's).

Cf. A002110, A053589, A111701, A328479.

Cf. also A093411 for analogous sequence.

Programs

Mathematica

A111701[n_] := A111701[n] = Block[{m = n, k = 1}, While[IntegerQ[m/Prime[k]], m = m/Prime[k]; k++]; m];
a[n_] := a[n] = If[A111701[n] == n, n, a[A111701[n]]];
Array[a, 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))); };

Formula

If A111701(n) == n, then a(n) = n, otherwise a(n) = a(A111701(n)).

a(n) = n / A328479(n).

Extensions

Definition clarified by N. J. A. Sloane, Jan 19 2021