Canada perfect numbers

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Canada perfect numbers are numbers such that the sum of each base 10 digit squared adds up to the sum of the nontrivial divisors. The Canada perfect numbers are 125, 581, 8549 and 16999 (see A070308). These numbers were defined by mathematicians at the University of Manitoba to celebrate Canada's 125^th anniversary.

For example, with 125, we have $1^{2}+2^{2}+5^{2}=30$. The divisors of 125 are 1, 5, 25, and 125, and we see that 5 and 25 ad up to 30. Prime numbers are excluded from consideration since their nontrivial divisors add up to 0.

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 125, p. 43, Ellipses, Paris 2008.