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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 V. Shevelev, A question concerning perfect numbers 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 (PARI) is(n)=sumdiv(n, d, if(hammingweight(d)%2==0 && d

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Last modified December 10 12:10 EST 2023. Contains 367710 sequences. (Running on oeis4.)