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

1,1

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

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

Mathematica

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

Prog

(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

Crossrefs

Similar to but different from A239278.

Cf. A007947, A020639, A053669, A284721.

Even bisection of A355001.

Sequence in context: A282270 A013606 A206550 * A190911 A204903 A054906

Adjacent sequences: A284720 A284721 A284722 * A284724 A284725 A284726

Keyword

nonn

Author

N. J. A. Sloane, Apr 04 2017

Status

approved