A229291 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.

2, 3, 5, 7, 11, 23, 31, 43, 47, 67, 71, 139, 151, 211, 283, 311, 331, 431, 463, 659, 683, 691, 863, 907, 947, 967, 1051, 1151, 1291, 1303, 1319, 1367, 1427, 1511, 1699, 1867, 1979, 1987, 2011, 2111, 2131, 2311, 2351, 2531, 3011, 3023, 3083, 3323, 3851, 4099

Offset: 1

Author

José María Grau Ribas, Oct 06 2013

Keywords

• nonn

Comments

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

Crossrefs

Cf. A112765, A226963, A229289, A229290.

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[5]