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

Author

Colin Barker, Nov 12 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A247081, A250094.

Programs

Mathematica

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

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