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A260299 Numbers k such that hyperfactorial(prime(k)-1) == 1 (mod prime(k)). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A271645 A265483 A154906 * A080623 A196260 A073814

Adjacent sequences:  A260296 A260297 A260298 * A260300 A260301 A260302

KEYWORD

nonn

AUTHOR

Matthew Campbell, Jul 22 2015

STATUS

approved

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)