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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A053669, A381031, A381113.

Cf. also A351566.

Sequence in context: A160585 A307447 A016658 * A331210 A330874 A372561

Adjacent sequences: A380536 A380537 A380538 * A380540 A380541 A380542

Keyword

nonn

Author

Antti Karttunen, Feb 12 2025

Status

approved