A250095 Positive integers k such that the numerator of the harmonic mean of the proper divisors of k is equal to k.

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

Offset

1,1

Links

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

Example

27 is a term because the proper divisors of 27 are [1,3,9] and 3 / (1/1 + 1/3 + 1/9) = 27/13.

Mathematica

Select[Range[668], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 1) * #/(DivisorSigma[1, #] - 1)] == # &] (* Amiram Eldar, Mar 02 2020 *)

Prog

(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

Crossrefs

Cf. A247081, A250094.

Sequence in context: A176031 A093845 A351747 * A085702 A068349 A129204

Adjacent sequences: A250092 A250093 A250094 * A250096 A250097 A250098

Keyword

nonn

Author

Colin Barker, Nov 12 2014

Status

approved