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%I #14 Jun 15 2021 01:44:52
%S 1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,
%T 7560,10080,15120,20160,25200,27720,45360,50400,55440,83160,110880,
%U 166320,221760,277200,332640,498960,554400,665280,720720,1081080,1441440,2162160,2882880
%N Union of the highly composite and superabundant numbers.
%C Numbers m that set records in A000005 and numbers k that set records for the ratio A000203(k)/k, sorted, with duplicates removed.
%C All terms are in A025487, since all terms in A002182 and A004394 are products of primorials P in A002110.
%C For numbers that are highly composite but not superabundant, see A308913; for numbers that are superabundant but not highly composite, see A166735. - _Jon E. Schoenfield_, Jun 14 2021
%H Michael De Vlieger, <a href="/A340840/b340840.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A340840/a340840.png">Annotated scatterplot of a(n) = A301414(x) * A002110(y) at (x, y)</a> showing the intersection A166981 of A002182 and A004394, and the intersection A224078 of A002201 and A004490.
%t (* Load the function f[] at A025487, then: *) Block[{t = Union@ Flatten@ f[15], a = {}, b = {}, d = 0, s = 0}, Do[(If[#2 > d, d = #2; AppendTo[a, #1]]; If[#3/#1 > s, s = #3/#1; AppendTo[b, #1]]) & @@ Flatten@ {t[[i]], DivisorSigma[{0, 1}, t[[i]]]}, {i, Length@ t}]; Union[a, b]]
%Y Cf. A000005, A000203, A027750, A002110.
%Y Supersets: A025487, A055932.
%Y Subsets: A002182, A002201, A004394, A004490, A166735, A166981, A168263, A189228, A224078, A304234, A304235, A308913, A333655, A338786.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Jan 27 2021
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