A247081 Positive integers k such that the numerator of the harmonic mean of the nontrivial divisors of k is equal to k.
8, 15, 18, 21, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 77, 81, 85, 87, 91, 93, 95, 99, 111, 115, 117, 119, 123, 128, 129, 133, 141, 143, 145, 147, 153, 155, 159, 161, 162, 171, 175, 177, 183, 185, 187, 201, 203, 205, 207, 209, 213, 215, 217, 219, 221, 235
Offset: 1
Keywords
Examples
18 is a term because the nontrivial divisors of 18 are [2,3,6,9] and 4 / (1/2 + 1/3 + 1/6 + 1/9) = 18/5.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Colin Barker)
Programs
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Mathematica
Select[Range[235], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 2) * #/(DivisorSigma[1, #] - # -1)] == # &] (* Amiram Eldar, Mar 02 2020 *)
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PARI
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k]) nontrivialdivisors(n) = d=divisors(n); vector(#d-2, k, d[k+1]) s=[]; for(n=2, 500, t=nontrivialdivisors(n); if(#t>0 && numerator(harmonicmean(t))==n, s=concat(s, n))); s
Comments