A260178 a(n) = hyperfactorial(prime(n)-1) mod prime(n).

1, 1, 3, 1, 10, 8, 13, 18, 22, 17, 30, 6, 9, 42, 1, 30, 1, 50, 66, 70, 27, 1, 1, 34, 22, 10, 1, 1, 76, 15, 1, 130, 37, 1, 105, 150, 28, 162, 166, 93, 178, 19, 1, 81, 14, 1, 1, 222, 226, 107, 144, 238, 64, 1, 16, 1, 82, 270, 60, 53, 1, 155, 1, 310, 288, 203, 1

Offset: 1

Author

Matthew Campbell, Jul 17 2015

Keywords

• nonn
• easy

Examples

			a(2) = hyperfactorial(2) mod 3 = (2^2*1^1) mod 3 = 4 mod 3 = 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 687 terms from Matthew Campbell)

Crossrefs

Cf. A000040, A002109, A260611.

Programs

Maple

a:= proc(n) option remember; local i, p, r, v;
      p, r, v:= ithprime(n), 1$2;
      for i from p-1 to 1 by -1 do
        v:= v*i mod p; r:= r*v mod p
      od; r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 21 2015

Mathematica

Table[Mod[Hyperfactorial[Prime[n] - 1], Prime[n]], {n, 1, 200}]

PARI

a(n,p=prime(n))=lift(prod(k=2,p-1,Mod(k,p)^k)) \\ Charles R Greathouse IV, Jul 23 2015

Formula

a(n) = A002109(A000040(n)-1) mod A000040(n).