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A284723 Smallest odd prime that is relatively prime to n. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)