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A329189
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3-admirable numbers: 3-abundant numbers (A068403) k such that exists a proper divisor d of k such that sigma(k) - 2*d = 3*k, where sigma(k) is the sum of divisors of k (A000203).
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4
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180, 240, 360, 420, 504, 540, 600, 780, 1080, 1344, 1872, 1890, 2016, 2184, 2352, 2376, 2688, 3192, 3276, 3744, 4284, 4320, 4680, 5292, 5376, 5796, 6048, 6552, 7128, 7344, 7440, 8190, 9504, 10296, 10416, 13776, 14850, 18600, 19824, 19872, 20496, 21528, 22932
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OFFSET
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1,1
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COMMENTS
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Analogous to admirable numbers (A111592) as 3-perfect numbers (A005820) are analogous to perfect numbers (A000396).
The proper divisors of each term k can be added to a sum of 2*k with one divisor taken with a minus sign.
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LINKS
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EXAMPLE
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180 is a term since its proper divisors can be added to 1 + 2 - 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 = 360 = 2 * 180, with one divisor, 3, taken with a minus sign.
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MATHEMATICA
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aQ[n_] := (ab = DivisorSigma[1, n] - 3 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2]; Select[Range[23000], aQ]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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