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A250095
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Positive integers k such that the numerator of the harmonic mean of the proper divisors of k is equal to k.
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3
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4, 27, 28, 54, 56, 64, 68, 91, 99, 100, 133, 138, 148, 154, 165, 188, 217, 222, 247, 259, 268, 276, 279, 290, 301, 308, 369, 375, 388, 403, 414, 427, 428, 430, 469, 474, 481, 508, 511, 540, 544, 548, 549, 553, 559, 589, 609, 621, 627, 628, 639, 642, 665, 668
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OFFSET
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1,1
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LINKS
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EXAMPLE
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27 is a term because the proper divisors of 27 are [1,3,9] and 3 / (1/1 + 1/3 + 1/9) = 27/13.
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MATHEMATICA
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Select[Range[668], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 1) * #/(DivisorSigma[1, #] - 1)] == # &] (* Amiram Eldar, Mar 02 2020 *)
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PROG
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(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
properdivisors(n) = d=divisors(n); vector(#d-1, k, d[k])
s=[]; for(n=2, 1000, if(numerator(harmonicmean(properdivisors(n)))==n, s=concat(s, n))); s
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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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