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

13967553600, 2248776129600, 65214507758400, 195643523275200, 12129898443062400, 448806242393308800, 18401055938125660800, 185942670254759802384000, 9854961523502269526352000, 1162885459773267804109536000, 780296143507862696557498656000

Offset: 1

Author

Michael De Vlieger, May 08 2018

Keywords

• nonn
• fini

Comments

Numbers m in A002201 that are also in A004394 but not A004490.

Subset of A166981. Numbers in this sequence are in neither A224078 nor A304235.

There are 39 terms in this sequence.

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}.

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.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..39
• Michael De Vlieger, Superior highly composite numbers m that are also superabundant but not colossally abundant
• Michael De Vlieger, Color coded plot of m A002182 and A004394 at (x,y) where A301414(x) * A002110(y) = m, terms in this sequence are colored dark blue.
• Michael De Vlieger, Annotated plot of a(n) for 1 <= n <= 39 at (x,y) = (a(n)/A002110(A001221(a(n)), A002110(A001221(a(n)))

Crossrefs

Cf. A002110, A002182, A002201, A004394, A004490, A166981, A224078, A304235.

Programs

Mathematica

(* First, download b-files at A002201, A004394, and A004490 *)
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]};
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, #] &]]