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%I #12 Jun 01 2020 01:57:19
%S 1,6,28,140,270,672,1638,2970,8190,27846,30240,167400,237510,332640,
%T 695520,1421280,2178540,2457000,11981970,14303520,17428320,23963940,
%U 27027000,46683000,56511000,71253000,142990848,163390500,164989440,191711520,400851360,407386980
%N Harmonic numbers (A001599) with a record harmonic mean of divisors.
%C The corresponding record values are 1, 2, 3, 5, 6, 8, 9, 11, 15, ... (see the link for more values).
%C The terms 1, 6, 30240 and 332640 are also terms of A179971.
%H Amiram Eldar, <a href="/A335316/b335316.txt">Table of n, a(n) for n = 1..70</a> (terms below 10^14)
%H Amiram Eldar, <a href="/A335316/a335316.txt">Table of n, a(n), A099377(a(n)) for n = 1..70</a>
%e The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their harmonic means of divisors (A001600) are 1, 2, 3, 5, 6, 5 and 8. The record values, 1, 2, 3, 5, 6 and 8 occur at 1, 6, 28, 140, 270 and 672, the first 6 terms of this sequence.
%t h[n_] := n * DivisorSigma[0, n] / DivisorSigma[1, n]; hm = 0; s = {}; Do[h1 = h[n]; If[IntegerQ[h1] && h1 > hm, hm = h1; AppendTo[s, n]], {n, 1, 10^6}]; s
%Y Cf. A001599, A001600, A099377, A099378, A179971, A335317, A335318.
%K nonn
%O 1,2
%A _Amiram Eldar_, May 31 2020
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