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%I #14 Nov 30 2020 10:57:33
%S 1,2,6,60,360,73513440,1396755360,4497552259200,130429015516800,
%T 149602080797769600,4488062423933088000,6133685312708553600,
%U 184010559381256608000,7912454053394034144000,19709923047004539052704000,1162885459773267804109536000,780296143507862696557498656000
%N Highly composite numbers (A002182) with a record number of largely composite numbers (A067128) having the same number of divisors.
%C The corresponding record numbers of divisors d(a(n)) are 1, 2, 3, 6, 9, 10, 11, 14, 16, 20, ... (see the link for more values).
%H Amiram Eldar, <a href="/A308532/b308532.txt">Table of n, a(n) for n = 1..25</a>
%H Amiram Eldar, <a href="/A308532/a308532.txt">Table of n, a(n), d(a(n)) for n = 1..25</a>
%e 6 is in the sequence since there are a record number of 3 largely composite numbers, 6, 8, and 10 with the same number of divisors. The next record is of 60, with 6 largely composite numbers, 60, 72, 84, 90, 96, and 108, with the same number of divisors.
%t s = {}; dm = 1; c = 0; cm = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c > cm, cm = c; AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^3}]; s
%Y Cf. A000005, A002182, A067128, A308530.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 06 2019