but no (*) proof about--the existence of odd versions of these numbers.
The aliquot sequence is constant for these numbers, whose examples other than the first one have digital root 1. Currently-known examples of them are in one-to-one correspondence with Mersenne prime numbers, and there are a number of restrictions on-- but no (*) proof about--the existence of odd versions of these numbers. Equaling the sum of its proper divisors, for 10 points, give this type of number whose first two examples are 6 and 28.
The aliquot sequence is constant for these numbers, whose examples other than the first one have digital root 1.
perfect numbers