A250094 - OEIS

%I #27 Jun 29 2022 09:16:38

%S 1,3,5,7,11,13,17,19,20,21,22,23,27,29,31,35,37,38,39,41,43,45,47,49,

%T 53,55,56,57,59,61,65,67,68,71,73,77,79,83,85,86,89,93,97,99,101,103,

%U 107,109,110,111,113,115,116,118,119,125,127,129,131,133,134

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

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

%C All odd primes are in this sequence.

%H Amiram Eldar, <a href="/A250094/b250094.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Colin Barker)

%e 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.

%t Select[Range[200],Numerator[HarmonicMean[Divisors[#]]]==#&] (* _Harvey P. Dale_, May 24 2017 *)

%t Select[Range[134], Numerator[DivisorSigma[0, #] * #/DivisorSigma[1, #]] == # &] (* _Amiram Eldar_, Mar 02 2020 *)

%o (PARI)

%o harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])

%o s=[]; for(n=1, 500, if(numerator(harmonicmean(divisors(n)))==n, s=concat(s, n))); s

%Y Cf. A099377, A247081, A250095.

%K nonn

%O 1,2

%A _Colin Barker_, Nov 12 2014