OFFSET
1,3
COMMENTS
Motivated by sequence A100083, numbers such that a(n) = 0. - Hasler
Note that this is a different sequence from A086330: in this one, the factorials are added up and then the remainder of the total divided by n is taken, whereas in A086330 each factorial is computed modulo n prior to being added up. - Alonso del Arte, Jun 11 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A086330(n) mod n. - Chai Wah Wu, Apr 16 2024
a(n) = Sum_{k=1..A002034(n)-2} (k+1)! mod n. - David A. Corneth, Apr 16 2024
EXAMPLE
a(3) = 2 because 2!, 3! and 4! are 2, 6 and 24 respectively, which add up to 32, and modulo 3 that is 2.
a(4) = 0 because 2!, 3!, 4! and 5! add up to 152, and modulo 4 that is 0 (note that this is different from A086330(4) = 4.
MATHEMATICA
Table[Mod[Sum[(k + 1)!, {k, n}], n], {n, 75}] (* Alonso del Arte, Jun 11 2013 *)
PROG
(PARI) a(n)=lift(sum(m=2, n-1, Mod(m!, n)))
(PARI) a(n)=my(t=Mod(1, n)); lift(sum(m=2, n+1, t*=m)) \\ Charles R Greathouse IV, Jun 11 2013
(Python)
def A226570(n):
a, c = 0, 1
for m in range(2, n):
c = c*m%n
if c==0:
break
a = (a+c)%n
return a # Chai Wah Wu, Apr 16 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jun 11 2013
STATUS
approved