A160994 - OEIS

%I #5 Jul 30 2024 14:35:36

%S 3,7,7,19,19,139,151,211,211,211,421,2311,2311,92401,120121,120121,

%T 180181,2312311

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

%t (* 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]];

%t 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 *)

%Y Cf. A093893, A093894.

%K nonn,more

%O 1,1

%A _Robert G. Wilson v_, Jun 01 2009

%E Offset changed to 1 and name corrected by _Amiram Eldar_, Jul 30 2024