A229290 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.

2, 3, 7, 19, 43, 127, 2287, 4903, 5419, 13723, 14479, 82339, 98299, 101347, 304039, 617767, 688087, 1676827, 3735583, 3736087, 4130323, 4324363, 4693267, 4951819, 10621603, 11032999, 11208259, 11554243, 11737783, 12198859, 26152603, 26563939, 28159603

Offset: 1

Author

José María Grau Ribas, Oct 05 2013

Keywords

• nonn

Comments

If n is in A226961 then n is some product of elements of this sequence.

Crossrefs

Cf. A007949, A226961, A229289, A229291.

Programs

Mathematica

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