

A230587


Number n such that the sum of its proper evil divisors (A001969) equals n.


2



18, 476, 1484, 1988, 2324, 3164, 4172, 4564, 5516, 7196, 7364, 7532, 8036, 8876, 9716, 9772, 10052, 10444, 10892, 11956, 12572, 13076, 13412, 14084, 16604, 16772, 18004, 19866, 20692, 21328, 21364, 21644, 22316, 22988, 23492, 23884, 23996, 24164, 24668, 24836
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OFFSET

1,1


COMMENTS

Sequence could be called the "evilperfect numbers".
By the EuclidEuler theorem, an even number n is perfect (A000396) if and only if n=2^(k1)*(2^k1), where 2^k1 is prime. From this it follows that all even perfect numbers more than 6 have only odious divisors (A000069). In contrast to them, this sequence lists those abundant numbers n (A005101), all proper evil divisors of which sum to n.
It is asked, are there nonperfect numbers n, all proper odious divisors of which sum to n? The first two such numbers were found by Giovanni Resta, see A212302.


LINKS



EXAMPLE

18 is in the sequence since its proper divisors are {1, 2, 3, 6, 9}, and their subset that is in A001969 is {3, 6, 9} whose sum is 18.


MATHEMATICA

aQ[n_] := DivisorSum[n, # &, # < n && EvenQ[DigitCount[#, 2][[1]]] &] == n; Select[Range[25000], aQ] (* Amiram Eldar, Jun 21 2019 *)


PROG



CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



