A260611 - OEIS

%I #10 Aug 05 2015 16:31:03

%S 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,

%T 106,76,15,126,1,37,138,105,1,28,1,1,93,1,19,190,81,14,198,210,1,1,

%U 107,144,1,64,250,16,262,82,1,60,53,282,155,306,1,288,203,330,189,1,136,42,1,366

%N a(n) = superfactorial(prime(n)-1) mod prime(n).

%H Matthew Campbell and Charles R Greathouse IV, <a href="/A260611/b260611.txt">Table of n, a(n) for n = 1..10000</a> (first 724 terms from Campbell)

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

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

%p a:= proc(n) option remember; local i, p, r, v;

%p       p, r, v:= ithprime(n), 1$2;

%p       for i from 2 to p-1 do

%p         v:= v*i mod p; r:= r*v mod p

%p       od; r

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 05 2015

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

%o (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

%Y The same for hyperfactorials: A260178.

%Y Cf. A000178, A000040.

%K nonn

%O 1,2

%A _Matthew Campbell_, Aug 05 2015