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

1,2

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.

Links

Table of n, a(n) for n=1..14.

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 *)

Prog

(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

Crossrefs

Cf. A007619, A050299, A157249.

Sequence in context: A192067 A347653 A288735 * A304433 A080707 A059612

Adjacent sequences: A317504 A317505 A317506 * A317508 A317509 A317510

Keyword

nonn,more

Author

Amiram Eldar, Sep 29 2018

Status

approved