A380539 The second smallest prime not dividing n.

3, 5, 5, 5, 3, 7, 3, 5, 5, 7, 3, 7, 3, 5, 7, 5, 3, 7, 3, 7, 5, 5, 3, 7, 3, 5, 5, 5, 3, 11, 3, 5, 5, 5, 3, 7, 3, 5, 5, 7, 3, 11, 3, 5, 7, 5, 3, 7, 3, 7, 5, 5, 3, 7, 3, 5, 5, 5, 3, 11, 3, 5, 5, 5, 3, 7, 3, 5, 5, 11, 3, 7, 3, 5, 7, 5, 3, 7, 3, 7, 5, 5, 3, 11, 3, 5, 5, 5, 3, 11, 3, 5, 5, 5, 3, 7, 3, 5, 5, 7, 3, 7, 3, 5, 11

Offset: 1

Author

Antti Karttunen, Feb 12 2025

Keywords

• nonn

Examples

			For n = 1, the least prime not dividing it is 2, and the second least prime not dividing is 3, thus a(1) = 3.
For n = 3, the least nondividing prime is 2, the second least nondividing prime is 5, thus a(3) = 5.
For n = 6 = 2*3, the least nondividing prime is 5, and the second least nondividing prime is 7, thus a(6) = 7.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030

Crossrefs

Cf. A053669, A381031, A381113.

Cf. also A351566.

Programs

Mathematica

a[n_] := Module[{p = 1, c = 0}, While[c < 2, p = NextPrime[p]; If[! Divisible[n, p], c++]]; p]; Array[a, 105] (* Amiram Eldar, Feb 14 2025 *)

PARI

A380539(n) = { my(c=0); forprime(p=2, , if(n%p, c++; if(2==c, return(p)))); };

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5.159142... (A381113). - Amiram Eldar, Feb 14 2025