A304234 - OEIS

A304234

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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)))

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, #] &]]

CROSSREFS

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

Sequence in context: A017364 A017484 A017616 * A134298 A046060 A172595

Adjacent sequences: A304231 A304232 A304233 * A304235 A304236 A304237

KEYWORD

nonn,fini

AUTHOR

Michael De Vlieger, May 08 2018

STATUS

approved