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A338786 Numbers in A166981 that are neither superior highly composite nor colossally abundant.

%I A338786 #16 Dec 28 2020 17:51:13
%S A338786 1,4,24,36,48,180,240,720,840,1260,1680,10080,15120,25200,27720,
%T A338786 110880,166320,277200,332640,554400,665280,2162160,3603600,7207200,
%U A338786 8648640,10810800,36756720,61261200,73513440,122522400,147026880,183783600,698377680,735134400,1102701600
%N A338786 Numbers in A166981 that are neither superior highly composite nor colossally abundant.
%C A338786 These are numbers both highly composite and superabundant but neither superior highly composite nor colossally abundant.
%C A338786 This sequence, A224078, A304234, and A304235 are mutually exclusive subsets that comprise A166981.
%C A338786 Superset A166981 has 449 terms; this sequence has 358, A224078 has 20, A304234 has 39, and A304235 has 32.
%H A338786 Michael De Vlieger, <a href="/A338786/b338786.txt">Table of n, a(n) for n = 1..358</a>
%H A338786 Michael De Vlieger, <a href="/A338786/a338786.png">Annotated plot of a(n) at (x,y) = (a(n)/A002110(A001221(a(n)), A002110(A001221(a(n)))</a>
%H A338786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly Composite Number</a>
%H A338786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ColossallyAbundantNumber.html">Colossally Abundant Number</a>
%H A338786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SuperabundantNumber.html">Superabundant Number</a>
%H A338786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SuperiorHighlyCompositeNumber.html">Superior Highly Composite Number</a>
%F A338786 Complement of (the union of A002182 and A004394) and (the union of A002201 and A004490).
%e A338786 1 is in the sequence since it is the empty product, setting records for both the number of divisors and the sum of divisors, and it is neither also superior highly composite nor colossally abundant.
%e A338786 2 is not in the sequence since it is both colossally abundant and superior highly composite.
%e A338786 4 is in the sequence since it sets a record for the divisor counting and divisor sum functions, yet it is neither superior highly composite nor colossally abundant.
%e A338786 20951330400 is not in the sequence since it is colossally abundant though it is an HCN and SA. etc.
%t A338786 Complement[Import["https://oeis.org/A166981/b166981.txt", "Data"][[1 ;; 449, -1]], Union[FoldList[Times, Import["https://oeis.org/A073751/b073751.txt", "Data"][[1 ;; 120, -1]] ], FoldList[Times, Import["https://oeis.org/A000705/b000705.txt", "Data"][[1 ;; 120, -1]] ] ] ] (* Program reads OEIS b-files _Michael De Vlieger_, Nov 09 2020 *)
%Y A338786 Cf. A189228, A002201, A002182, A004394, A004490, A166981, A224078, A304234, A304235.
%K A338786 nonn,fini,full
%O A338786 1,2
%A A338786 _Michael De Vlieger_, Nov 09 2020