A284723 Smallest odd prime that is relatively prime to n.

3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3

Offset: 1

Author

N. J. A. Sloane, Apr 04 2017

Keywords

• nonn

Comments

More than the usual number of terms are shown in order to distinguish this from A239278.

a(n) = smallest odd prime missing from rad(n).

If rad(m) = rad(n), a(m) = a(n) (cf. A007947). - Bob Selcoe, Apr 04 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Similar to but different from A239278.

Cf. A007947, A020639, A053669, A284721.

Even bisection of A355001.

Programs

Mathematica

a[n_] := Module[{p = 3}, While[Divisible[n, p], p = NextPrime[p]]; p]; Array[a, 100] (* Amiram Eldar, Jul 25 2022 *)

PARI

a(n) = my(p=3); while(gcd(n, p) != 1, p=nextprime(p+1)); p; \\ Michel Marcus, Apr 04 2017; corrected Jun 13 2022

Formula

a(n) = 3 unless n == 0 (mod 3).

For n>3, a(n) < 3*log(n).

a(n) = A355001(2*n). - Antti Karttunen, Jul 18 2022

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p odd prime} ((p*(p-1)/Product_{q odd prime <= p} q)) = 3.8401019546... . - Amiram Eldar, Jul 25 2022