A260299 Numbers k such that hyperfactorial(prime(k)-1) == 1 (mod prime(k)).

1, 2, 4, 15, 17, 22, 23, 27, 28, 31, 34, 43, 46, 47, 54, 56, 61, 63, 67, 73, 75, 76, 83, 91, 92, 95, 96, 101, 107, 109, 111, 115, 117, 120, 129, 132, 141, 143, 144, 146, 149, 150, 153, 154, 155, 164, 167, 181, 190, 192, 193, 205, 208, 214, 215, 219, 224, 225

Offset

1,2

Links

Matthew Campbell and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2516 terms from Campbell)

Formula

a(n) = pi(A260298(n)).

Example

The 4th prime is 7, and the hyperfactorial of 7 is 4031078400000, which is congruent to 1 mod 7. - Kellen Myers, Aug 19 2015

Mathematica

PrimePi[fQ[n_]:= Mod[Hyperfactorial[n - 1], n] == 1; Select[Prime@Range@250, fQ]] (* Vincenzo Librandi, Aug 20 2015 *)

Prog

(PARI) is(n, p=prime(n))=prod(k=2, p-1, Mod(k, p)^k)==1 \\ Charles R Greathouse IV, Aug 29 2015

Crossrefs

Cf. A000040, A002109, A260178, A260297, A260298.

Sequence in context: A265483 A357692 A154906 * A080623 A196260 A073814

Adjacent sequences: A260296 A260297 A260298 * A260300 A260301 A260302

Keyword

nonn

Author

Matthew Campbell, Jul 22 2015

Status

approved