%I #11 Jun 01 2020 01:56:44
%S 1,6,28,140,270,672,2970,8190,30240,332640,2178540,2457000,11981970,
%T 14303520,17428320,27027000,163390500,164989440,191711520,513513000,
%U 1307124000,2144862720,2701389600,3506025600,5943057120,13584130560,14378364000,29715285600,45578332800
%N Harmonic numbers (A001599) with a record number of divisors.
%C The corresponding record values are 1, 4, 6, 12, 16, 24, 32, 48, 96, ... (see the link for more values).
%H Amiram Eldar, <a href="/A335317/b335317.txt">Table of n, a(n) for n = 1..40</a> (terms below 10^14)
%H Amiram Eldar, <a href="/A335317/a335317.txt">Table of n, a(n), A000005(a(n)) for n = 1..40</a>
%e The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their numbers of divisors (A000005) are 1, 4, 6, 12, 16, 10 and 24. The record values, 1, 4, 6, 12, 16 and 24 occur at 1, 6, 28, 140, 270 and 672, the first 6 terms of this sequence.
%t dm = 0; s = {}; Do[h = n * (d = DivisorSigma[0, n]) / DivisorSigma[1, n]; If[IntegerQ[h] && d > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s
%Y Cf. A000005, A001599, A335316, A335318.
%K nonn
%O 1,2
%A _Amiram Eldar_, May 31 2020