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

Author

Colin Barker, Nov 12 2014

Keywords

• nonn

Comments

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

All odd primes are in this sequence.

Examples

			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.
		

Links

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

Crossrefs

Cf. A099377, A247081, A250095.

Programs

Mathematica

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 *)

PARI

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