[seqfan] A question concerning perfect numbers

Vladimir Shevelev shevelev at bgu.ac.il
Thu Oct 24 12:13:58 CEST 2013

Dear SeqFans,
By best known Euclid-Euler theorem, an even n is a perfect
number (A000396) if and only if it has form 2^(k-1)*(2^k-1),
where 2^k-1 is prime. From this it follows that all even perfect numbers, except for 6, have only odious divisors (A000069).
Consider number n, for which all its proper odious divisors
sum to n. The first such a number is perfect number 28. I 
asked Peter to find a few such numbers, but up to 10^5 he found only three: 28,496,8128 which all are perfect numbers.
My question is: are there non-perfect such numbers?
Note, that there are respectively "many" numbers n, for which all their proper evil divisors sum to n (we submit sequence A230587).
Best regards,

 Shevelev Vladimir‎

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