A210185 Sum of distinct residues of all factorials mod prime(n).

1, 3, 7, 12, 24, 56, 97, 103, 156, 224, 341, 494, 608, 521, 732, 821, 997, 1412, 1312, 1228, 1592, 1984, 2212, 2503, 2583, 3158, 3644, 3846, 3309, 4004, 5149, 5394, 6214, 6129, 7667, 6371, 8100, 8320, 8464, 9174, 10195, 10083, 11973, 11660, 12174, 11530, 14053

Offset: 1

Author

Vladimir Shevelev, Mar 18 2012

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040, A000142, A210184.

Programs

Mathematica

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

PARI

a(n) = my(p=prime(n)); vecsum(Set(vector(p, k, k! % p))); \\ Michel Marcus, Dec 15 2018