A267505 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 13 are also in the sequence.

2, 3, 7, 43, 79, 547, 3319, 6163, 36979, 42667, 258847, 1553119, 1573207, 1834639, 1854763, 11131927, 20224159, 20451679, 124027567, 141569107, 141588763, 467477683, 1840398379, 3278780359, 5276533183, 6089163523, 6155955079, 11168428363, 11185512199, 31655671459

Offset: 1

Author

José María Grau Ribas, Jan 16 2016

Keywords

• nonn

Comments

Is this sequence infinite?

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A267503, A267504, A267506, A267507, A005117, A227455, A227007, A227006.

Programs

Mathematica

fa = FactorInteger; is[2, p_] = True; is[2, p_];
is[n_, p_] := PrimeQ[n] &&  MoebiusMu[n - 1] ≠ 0 && Union@Table[is[fa[n - 1][[i, 1]], p] || fa[n - 1][[ i, 1]] == p , {i, Length[fa[n - 1]]}] == {True}; Select[Prime[Range[100000]], is[#, 13] &]

PARI

leastdiv(v, pred, inf)={ \\ finds least divisor d satisfying pred(d) && d>=inf
  my(recurse(k,d,lim)= if(d >= lim, lim, if(d>=inf && pred(d), d, k++; if(k<=#v, lim=self()(k, d*v[k], lim); self()(k, d, lim), lim))));
  my(stop=vecprod(v), lim=inf, m=4);
  while(lim<=stop, lim*=m; my(d=recurse(0,1,lim)); if(disprime(d+1), S[#S]); if(t==oo, break); t++; print1(t, ", "))} \\ Andrew Howroyd, Nov 13 2018

Extensions

Terms a(16) and beyond from Andrew Howroyd, Nov 13 2018