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

1,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A000142, A210184.

Sequence in context: A226229 A167491 A356807 * A280345 A062325 A301982

Adjacent sequences: A210182 A210183 A210184 * A210186 A210187 A210188

Keyword

nonn

Author

Vladimir Shevelev, Mar 18 2012

Status

approved