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A304234
Superior highly composite numbers that are superabundant but not colossally abundant.
5
13967553600, 2248776129600, 65214507758400, 195643523275200, 12129898443062400, 448806242393308800, 18401055938125660800, 185942670254759802384000, 9854961523502269526352000, 1162885459773267804109536000, 780296143507862696557498656000
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, 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, #] &]]
KEYWORD
nonn,fini
AUTHOR
Michael De Vlieger, May 08 2018
STATUS
approved