

A210184


Number of distinct residues of all factorials mod prime(n).


5



2, 3, 4, 5, 6, 10, 12, 12, 17, 19, 21, 26, 29, 26, 31, 35, 37, 41, 42, 39, 44, 49, 55, 59, 59, 65, 71, 75, 63, 73, 80, 82, 90, 90, 104, 86, 103, 104, 107, 111, 113, 114, 120, 125, 120, 115, 139, 149, 132, 141, 147, 150, 147, 164, 166, 172, 172, 170, 172, 180
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OFFSET

1,1


COMMENTS

Conjecture: a(n)/p_n > 1/2.
The standard (folklore?) conjecture is that a(n)/prime(n) = 1  1/e = 0.63212....  Charles R Greathouse IV, May 11 2015


LINKS



EXAMPLE

Let n=4, p_4=7. We have modulo 7: 1!==1, 2!==2, 3!==6, 4!==3, 5!==1, 6!==6 and for m>=7, m!==0, such that we have 5 distinct residues 0,1,2,3,6. Therefore a(4) = 5.


MAPLE

a:= proc(n) local p, m, i, s;
p:= ithprime(n);
m:= 1;
s:= {};
for i to p do m:= m*i mod p; s:=s union {m} od;
nops(s)
end:


MATHEMATICA

Table[Length[Union[Mod[Range[Prime[n]]!, Prime[n]]]], {n, 100}] (* T. D. Noe, Mar 18 2012 *)


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



