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%I #33 Nov 02 2021 16:44:31
%S 20,21,22,27,35,38,39,45,49,55,56,57,65,68,77,85,86,93,99,110,111,115,
%T 116,118,119,125,129,133,134,143,147,150,155,161,164,166,169,183,184,
%U 185,187,189,201,203,205,207,209,212,214,215,217,219,221,235,237,245
%N Composite numbers k such that the numerator of the harmonic mean of the divisors of k is equal to k.
%C Composite numbers k such that A099377(k) = k.
%C Since the harmonic mean of the divisors of an odd prime p is p/((p+1)/2), its numerator is equal to p. Therefore, this sequence is restricted to composite numbers.
%C This sequence is infinite. For example, if p is a prime of the form 8*k+3 (A007520) with k>1, then 2*p is a term.
%H Amiram Eldar, <a href="/A346400/b346400.txt">Table of n, a(n) for n = 1..10000</a>
%e 20 is a term since the harmonic mean of the divisors of 20 is 20/7.
%t q[n_] := CompositeQ[n] && Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]] == n; Select[Range[250], q]
%o (PARI) isok(k) = my(d=divisors(k)); (#d>2) && (numerator(#d/sum(i=1, #d, 1/d[i])) == k); \\ _Michel Marcus_, Nov 01 2021
%o (PARI) list(lim)=my(v=List()); forfactored(n=20,lim\1, if(vecsum(n[2][,2])>1 && numerator(sigma(n,0)/sigma(n,-1))==n[1], listput(v,n[1]))); Vec(v) \\ _Charles R Greathouse IV_, Nov 01 2021
%Y Intersection of A002808 and A250094.
%Y Cf. A099377, A099378.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 01 2021