A089090 a(n) is the smallest composite number coprime to n.

4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 9, 4, 25, 4

Offset: 1

Author

Labos Elemer, Nov 26 2003

Keywords

• easy
• nonn

Comments

If n is the n-th primorial, then a(n) = prime(n+1)^2.

Examples

			n=30: below 30 coprimes to 30 phi(30)=8 numbers are relevant but each 1 or primes; so a(8)>30; the first suitable number is a(30)=49.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A053669, A007978, A053670-A053674, A090091-A090093.

Programs

Mathematica

m=0;Table[fla=1;Do[s=GCD[n, k];If[Equal[s, 1]&&!PrimeQ[n]&&!Equal[n, 1]&& Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 130}], {k, 1, 256}]

PARI

A089090(n) = forprime(p=2, , if(n%p, return(p*p))); \\ Antti Karttunen, Dec 19 2018

Formula

a(n) = A053669(n)^2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} ((p^2*(p-1)/Product_{q prime <= p} q)) = 10.3344588090... . - Amiram Eldar, Jul 25 2022

Extensions

Offset corrected by Antti Karttunen, Dec 19 2018