A379768 a(n) is the smallest prime p such that omega(p^n + 1) = n.

2, 3, 5, 43, 17, 47, 151, 1697, 59, 2153, 521, 13183, 30089, 66569, 761

Offset: 1

Author

Daniel Suteu, Jan 06 2025

Keywords

• nonn
• more
• hard

Comments

2*10^6 < a(16) <= 206874667; a(18) = 33577; a(20) <= 3258569.

A219018(n) <= a(n) <= A280005(n).

Examples

			a(3) = 5 is the smallest prime of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.
		

Crossrefs

Cf. A001221, A219018, A242786, A280005, A362957, A379450.

Programs

Mathematica

a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]

PARI

a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));