Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jul 07 2015 22:19:56
%S 2,3,7,19,43,127,2287,4903,5419,13723,14479,82339,98299,101347,304039,
%T 617767,688087,1676827,3735583,3736087,4130323,4324363,4693267,
%U 4951819,10621603,11032999,11208259,11554243,11737783,12198859,26152603,26563939,28159603
%N n is in the sequence if n is prime, (n-1)/3^A007949(n-1) is a squarefree number, A007949(n-1) < 3 and every prime divisor of n-1 is in the sequence.
%C If n is in A226961 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[3]
%Y Cf. A007949, A226961, A229289, A229291.
%K nonn
%O 1,1
%A _José María Grau Ribas_, Oct 05 2013