OFFSET
0,2
COMMENTS
Also set of all n>=0, excluding 3, for which n+1 is composite. [Proof: (i) If n+1 is prime, there cannot be any factor in n! to cancel the n+1 in the denominator of the expression. (ii) If n+1=composite=a*b, a<b, consider the equivalent expression (n+1)!/(n+1)^2=1*2*..*a*..*b*..(a*b)/(a^2*b^2) in which factors obviously cancel. (iii) If n+1=square=a^2, a>2, (n+1)!/(n+1)^2 = 1*2*..*a*...*(2a)*..*a^2/a^4 in which factors also cancel.] - R. J. Mathar, Nov 22 2006
FORMULA
a(n) = A002808(n+1)-1 for n>=1. - R. J. Mathar, Nov 22 2006
EXAMPLE
n=5 5!/(5+1)= 5*4*3*2*1/6 = 20.
MAPLE
P:=proc(n) local i, j; for i from 0 by 1 to n do j:=i!/(i+1); if trunc(j)=j then print(i); fi; od; end: P(200);
MATHEMATICA
Select[Range[0, 100], IntegerQ[#!/(#+1)]&] (* Harvey P. Dale, Aug 24 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, May 22 2006
EXTENSIONS
Corrected (39 inserted) by Harvey P. Dale, Aug 24 2014
STATUS
approved