A317507 Numbers k whose generalized Wilson quotient A157249(k) is prime.

1, 5, 7, 8, 10, 11, 29, 62, 486, 614, 773, 1321, 1906, 2621

Offset: 1

Author

Amiram Eldar, Sep 29 2018

Keywords

• nonn
• more

Comments

The corresponding primes are 2, 5, 103, 13, 19, 329891, ...

Supersequence of A050299 (except for 1, the prime terms of this sequence).

No more terms below 10^4.

Crossrefs

Cf. A007619, A050299, A157249.

Programs

Mathematica

p[n_] := Times @@ Select[Range[n], CoprimeQ[n, #] &]; e[1 | 2 | 4] = 1; e[n_] := (fi = FactorInteger[n]; If[MatchQ[fi, {{(p_)?OddQ, }} | {{2, 1}, {, }}], 1, -1]); a[n] := (p[n] + e[n])/n; n = 1; s={}; Do[If[PrimeQ[a[n]], AppendTo[s,n]], {n, 1, 1000}]; s (* after Jean-François Alcover at A157249 *)

PARI

phito(n) = prod(k=2, n-1, k^(gcd(k, n)==1)); \\ A001783
is(n) = if(n%2, isprimepower(n) || n==1, n==2 || n==4 || (isprimepower(n/2, &n) && n>2)); \\ A033948
e(n) = if (is(n), 1, -1);
gw(n) = (phito(n)+e(n))/n;
isok(n) = isprime(gw(n)); \\ Michel Marcus, Oct 28 2018