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

Author

Matthew Campbell, Aug 05 2015

Keywords

• nonn

Examples

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

Links

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

Crossrefs

The same for hyperfactorials: A260178.

Cf. A000178, A000040.

Programs

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}]

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

Formula

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