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A230587
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Number n such that the sum of its proper evil divisors (A001969) equals n.
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2
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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
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1,1
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COMMENTS
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Sequence could be called the "evil-perfect numbers".
By the Euclid-Euler theorem, an even number n is perfect (A000396) if and only if n=2^(k-1)*(2^k-1), where 2^k-1 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 non-perfect numbers n, all proper odious divisors of which sum to n? The first two such numbers were found by Giovanni Resta, see A212302.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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aQ[n_] := DivisorSum[n, # &, # < n && EvenQ[DigitCount[#, 2][[1]]] &] == n; Select[Range[25000], aQ] (* Amiram Eldar, Jun 21 2019 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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