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

1,1

Comments

No primes are in this sequence.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A250094, A250095.

Sequence in context: A179107 A160524 A161541 * A133157 A014544 A237610

Adjacent sequences: A247078 A247079 A247080 * A247082 A247083 A247084

Keyword

nonn

Author

Colin Barker, Nov 17 2014

Status

approved