cp's OEIS Frontend

A304234 Superior highly composite numbers that are superabundant but not colossally abundant.

%I A304234 #16 Dec 28 2020 17:50:42
%S A304234 13967553600,2248776129600,65214507758400,195643523275200,
%T A304234 12129898443062400,448806242393308800,18401055938125660800,
%U A304234 185942670254759802384000,9854961523502269526352000,1162885459773267804109536000,780296143507862696557498656000
%N A304234 Superior highly composite numbers that are superabundant but not colossally abundant.
%C A304234 Numbers m in A002201 that are also in A004394 but not A004490.
%C A304234 Subset of A166981. Numbers in this sequence are in neither A224078 nor A304235.
%C A304234 There are 39 terms in this sequence.
%C A304234 The smallest term is 2^5 * 3^2 * 5 * A002110(8) or the product of A002110(k) with k = {1,1,1,2,3,8}.
%C A304234 The largest is 2^10 * 3^6 * 5^3 * 7^2 * 11 * 13 * 17 * 19 * 23 * A002110(65) or the product of A002110(k) with k = {1,1,1,1,2,2,2,3,4,9,65}, a 144 digit decimal number.
%H A304234 Michael De Vlieger, <a href="/A304234/b304234.txt">Table of n, a(n) for n = 1..39</a>
%H A304234 Michael De Vlieger, <a href="/A304234/a304234.txt">Superior highly composite numbers m that are also superabundant but not colossally abundant</a>
%H A304234 Michael De Vlieger, <a href="/A304234/a304234.png">Color coded plot of m A002182 and A004394 at (x,y) where A301414(x) * A002110(y) = m</a>, terms in this sequence are colored dark blue.
%H A304234 Michael De Vlieger, <a href="/A304234/a304234_1.png">Annotated plot of a(n)</a> for 1 <= n <= 39 at (x,y) = (a(n)/A002110(A001221(a(n)), A002110(A001221(a(n)))
%t A304234 (* First, download b-files at A002201, A004394, and A004490 *)
%t A304234 f[w_] := Times @@ Flatten@ {Complement[#1, Union[#2, #3]], Product[Prime@ i, {i, PrimePi@ #}] & /@ #2, Factorial /@ #3} & @@ ToExpression@ {StringSplit[w, _?(! DigitQ@ # &)], StringCases[w, (x : DigitCharacter ..) ~~ "#" :> x], StringCases[w, (x : DigitCharacter ..) ~~ "!" :> x]};
%t A304234 With[{s = Import["b002201.txt", "Data"][[All, -1]], t = Select[Map[Which[StringTake[#, 1] == {"#"}, f@ Last@ StringSplit@ Last@ #, StringTake[#, 1] == {}, Nothing, True, ToExpression@ StringSplit[#][[1, -1]]] &, Drop[Import["b004394.txt", "Data"], 3] ], IntegerQ@ First@ # &][[All, -1]], u = Import["b004490.txt", "Data"][[All, -1]]}, Select[Intersection[s, t], FreeQ[u, #] &]]
%Y A304234 Cf. A002110, A002182, A002201, A004394, A004490, A166981, A224078, A304235.
%K A304234 nonn,fini
%O A304234 1,1
%A A304234 _Michael De Vlieger_, May 08 2018