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

1,1

Comments

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

Links

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

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

Example

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.

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}]

Prog

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

Crossrefs

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

Sequence in context: A071793 A010714 A284018 * A204919 A113484 A061767

Adjacent sequences: A089087 A089088 A089089 * A089091 A089092 A089093

Keyword

easy,nonn

Author

Labos Elemer, Nov 26 2003

Extensions

Offset corrected by Antti Karttunen, Dec 19 2018

Status

approved