A250095 -id:A250095 - cp's OEIS frontend

A250094 Positive integers k such that the numerator of the harmonic mean of the divisors of k is equal to k.

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

Offset: 1

Colin Barker, Nov 12 2014

nonn

A subsequence of A099377: n such that A099377(n) = n.

All odd primes are in this sequence.

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Colin Barker)

Cf. A099377, A247081, A250095.

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 *)

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

A247081 Positive integers k such that the numerator of the harmonic mean of the nontrivial divisors of k is equal to k.

Original entry on oeis.org

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

Colin Barker, Nov 17 2014

nonn

No primes are in this sequence.

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Colin Barker)

Cf. A250094, A250095.

Select[Range[235], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 2) * #/(DivisorSigma[1, #] - # -1)] == # &] (* Amiram Eldar, Mar 02 2020 *)

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

cp's OEIS Frontend

A250094 Positive integers k such that the numerator of the harmonic mean of the divisors of k is equal to k.

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