Armstrong number | exponential digital invariant | perfect digital invariant | plus perfect number

An n-digit number that is the sum of the nth powers of its digits is called an n-narcissistic number. It is also sometimes known as an Armstrong number, perfect digital invariant, or plus perfect number. Hardy wrote, "There are just four numbers, after unity, which are the sums of the cubes of their digits: 153 = 1^3 + 5^3 + 3^3, 370 = 3^3 + 7^3 + 0^3, 371 = 3^3 + 7^3 + 1^3, and 407 = 4^3 + 0^3 + 7^3. These are odd facts, very suitable for puzzle columns and likely to amuse amateurs, but there is nothing in them which appeals to the mathematician." Narcissistic numbers therefore generalize these "unappealing" numbers to other powers.

additive persistence | digitaddition | digital root | Harshad number | Kaprekar number | Münchhausen number | multiplicative digital root | multiplicative persistence | powerful number | recurring digital invariant | vampire number