A210185 - OEIS

%I #20 Sep 14 2019 06:36:19

%S 1,3,7,12,24,56,97,103,156,224,341,494,608,521,732,821,997,1412,1312,

%T 1228,1592,1984,2212,2503,2583,3158,3644,3846,3309,4004,5149,5394,

%U 6214,6129,7667,6371,8100,8320,8464,9174,10195,10083,11973,11660,12174,11530,14053

%N Sum of distinct residues of all factorials mod prime(n).

%H Amiram Eldar, <a href="/A210185/b210185.txt">Table of n, a(n) for n = 1..2000</a>

%e 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)=0+1+2+3+6=12.

%t Table[Total[Union[Mod[Range[Prime[n]]!, Prime[n]]]], {n, 100}] (* _T. D. Noe_, Mar 18 2012 *)

%o (PARI) a(n) = my(p=prime(n)); vecsum(Set(vector(p, k, k! % p))); \\ _Michel Marcus_, Dec 15 2018

%Y Cf. A000040, A000142, A210184.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Mar 18 2012