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

1,1

Comments

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

Links

Table of n, a(n) for n=1..50.

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]

Crossrefs

Cf. A112765, A226963, A229289, A229290.

Sequence in context: A118721 A094318 A019344 * A057459 A068853 A328076

Adjacent sequences: A229288 A229289 A229290 * A229292 A229293 A229294

Keyword

nonn

Author

José María Grau Ribas, Oct 06 2013

Status

approved