Has this conjecture been proven/disproven/found before? My 11-year-old son has made the following conjecture, and wants to know if it's already known to be true or false:
if n is a whole number,
    define an operation #(n) = 1+2+3…..+n (like factorial but with addition)
    The conjecture: if n is odd, then #(n-1) = X*n (where X may be any natural number). That is, #(n-1) should be evenly divisible by n.

Hint: $1+2+...+n=\sum\limits_{k=1}^nk=\dfrac{n(n+1)}{2}$
