A229291 - OEIS

%I #21 Jul 03 2017 14:22:29

%S 2,3,5,7,11,23,31,43,47,67,71,139,151,211,283,311,331,431,463,659,683,

%T 691,863,907,947,967,1051,1151,1291,1303,1319,1367,1427,1511,1699,

%U 1867,1979,1987,2011,2111,2131,2311,2351,2531,3011,3023,3083,3323,3851,4099

%N n is in the sequence if n is prime, (n-1)/5^A112765(n-1) is a squarefree number, A112765(n-1) < 3 and every prime divisor of n-1 is in the sequence.

%C If n is in A226963 then n is some product of elements of this sequence.

%t fa = FactorInteger; free[n_] := n == Product[fa[n][[i, 1]], {i,

%t   Length[fa[n]]}]; Os[b_, 1] = True; Os[b_, 2] = True; Os[ b_, b_] = True; Os[b_, n_] := Os[b, n] = PrimeQ[n] && free[(n - 1)/b^IntegerExponent[n - 1,b]] && IntegerExponent[n - 1, b] < 3 && Union@Table[Os[b, fa[n - 1][[i, 1]]], {i, Length[fa[n - 1]]}] == {True}; G[b_] := Select[Prime [Range[2000]], Os[b, #] &]; G[5]

%Y Cf. A112765, A226963, A229289, A229290.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Oct 06 2013