A260611 a(n) = superfactorial(prime(n)-1) mod prime(n).

1, 2, 3, 6, 1, 8, 13, 1, 1, 17, 1, 6, 9, 1, 46, 30, 58, 50, 1, 1, 27, 78, 82, 34, 22, 10, 102, 106, 76, 15, 126, 1, 37, 138, 105, 1, 28, 1, 1, 93, 1, 19, 190, 81, 14, 198, 210, 1, 1, 107, 144, 1, 64, 250, 16, 262, 82, 1, 60, 53, 282, 155, 306, 1, 288, 203, 330, 189, 1, 136, 42, 1, 366

Offset

1,2

Links

Matthew Campbell and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 724 terms from Campbell)

Formula

a(n) = A000178(A000040(n)-1) mod A000040(n).

Example

a(2) = superfactorial(2) mod 3 = (2!*1!) mod 3 = 2 mod 3 = 2.

Maple

a:= proc(n) option remember; local i, p, r, v;
      p, r, v:= ithprime(n), 1$2;
      for i from 2 to p-1 do
        v:= v*i mod p; r:= r*v mod p
      od; r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 05 2015

Mathematica

Table[Mod[Superfactorial[Prime[n] - 1], Prime[n]], {n, 1, 175}]

Prog

(PARI) a(n, p=prime(n))=my(t=Mod(1, p)); lift(prod(k=2, p-1, t*=k)) \\ Charles R Greathouse IV, Aug 05 2015

Crossrefs

The same for hyperfactorials: A260178.

Cf. A000178, A000040.

Sequence in context: A346560 A084459 A093095 * A263502 A002171 A138515

Adjacent sequences: A260608 A260609 A260610 * A260612 A260613 A260614

Keyword

nonn

Author

Matthew Campbell, Aug 05 2015

Status

approved