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A250094
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Positive integers k such that the numerator of the harmonic mean of the divisors of k is equal to k.
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5
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1, 3, 5, 7, 11, 13, 17, 19, 20, 21, 22, 23, 27, 29, 31, 35, 37, 38, 39, 41, 43, 45, 47, 49, 53, 55, 56, 57, 59, 61, 65, 67, 68, 71, 73, 77, 79, 83, 85, 86, 89, 93, 97, 99, 101, 103, 107, 109, 110, 111, 113, 115, 116, 118, 119, 125, 127, 129, 131, 133, 134
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OFFSET
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1,2
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COMMENTS
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All odd primes are in this sequence.
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LINKS
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EXAMPLE
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20 is a term because the divisors of 20 are [1,2,4,5,10,20] and 6 / (1/1 + 1/2 + 1/4 + 1/5 + 1/10 + 1/20) = 20/7.
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MATHEMATICA
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Select[Range[200], Numerator[HarmonicMean[Divisors[#]]]==#&] (* Harvey P. Dale, May 24 2017 *)
Select[Range[134], Numerator[DivisorSigma[0, #] * #/DivisorSigma[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])
s=[]; for(n=1, 500, if(numerator(harmonicmean(divisors(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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