A160994 a(n) is the least prime number p such that every sum of two or more divisors of p^n is composite.

3, 7, 7, 19, 19, 139, 151, 211, 211, 211, 421, 2311, 2311, 92401, 120121, 120121, 180181, 2312311

Offset: 1

Author

Robert G. Wilson v, Jun 01 2009

Keywords

• nonn
• more

Crossrefs

Cf. A093893, A093894.

Programs

Mathematica

(* first do *) Needs["Combinatorica`"] (* then *) f[n_] := Block[{d = Divisors@n, k, mx}, k = 1 + Length@d; mx = 2^Length[d]; While[k < mx && !PrimeQ[Plus @@ NthSubset[k, d]], k++ ]; If[k == mx, Length@d, 0]];
a[n_] := a[n] = Module[{p = If[n == 1, 2, a[n-1]]}, While[f[p^n] == 0, p = NextPrime[p]]; p]; Array[a, 13] (* second part of the program added by Amiram Eldar, Jul 30 2024 *)

Extensions

Offset changed to 1 and name corrected by Amiram Eldar, Jul 30 2024