666 is an abundant number. It is the sum of the squares of the first seven prime numbers.
Since 36 is both square and triangular, 666 is the sixth number of the form
n2(n2 + 1) / 2 (triangular squares) and the eighth number of the form n(n + 1)(n2 + n + 2) / 8 (doubly triangular numbers.)
There is no number whose value of
Euler's totient function ö is 666, making it a nontotient.
The harmonic mean of the digits of 666 is an integer: 3/(
1/6 + 1/6 + 1/6) = 6. 666 is the 54th number with this property.
In base 10, 666 is a palindromic number, a repdigit and a
Smith number. A prime reciprocal magic square based on 1/
149 in base 10 has a magic total of 666.
The Roman numeral representation of the number 666 (
DCLXVI) uses once each the Roman numeral symbols with values under 1,000, and they occur in exact
reverse order of their respective values (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1).
I had no idea that the
number 666 had any relavance to a
legitimate mathmatical
formula!
