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a(n) = A002182(n)/A002110(A108602(n)).
8

%I #15 Oct 12 2023 01:53:26

%S 1,1,2,1,2,4,6,8,2,4,6,8,12,24,4,6,8,12,24,36,48,72,96,120,12,216,240,

%T 24,36,48,72,96,120,144,216,240,288,24,36,48,72,96,120,144,216,240,

%U 288,360,480,576,720,1080,72,1440,120,144,216,240,288,360,480,576

%N a(n) = A002182(n)/A002110(A108602(n)).

%C This sequence appears in Siano paper, page 5 of 12, as the "variable part" v. - _Michael De Vlieger_, Oct 11 2023

%H Michael De Vlieger, <a href="/A301413/b301413.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="http://vincico.com/proof/A301414.html">On a graph of highly composite numbers</a>

%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.html">Highly composite numbers</a>

%H D. B. Siano and J. D. Siano, <a href="http://wwwhomes.uni-bielefeld.de/achim/julianmanuscript3.pdf">An Algorithm for Generating Highly Composite Numbers</a>, 1994.

%F a(n) = A002182(n)/A007947(A002182(n)).

%e Let m be a value in this sequence. The table below shows m*A002110(A108602(k)). Columns are A108602(k), rows are m whose products m*A002110(A108602(k)) appear in A002182 are in this sequence. Numbers in A002182 that also appear in A002201 are followed by (*).

%e 0 1 2 3 4 5 6 ...

%e +------------------------------------

%e 1 | 1* 2* 6*

%e 2 | 4 12* 60*

%e 4 | 24 120* 840

%e 6 | 36 180 1260

%e 8 | 48 240 1680

%e 12 | 360* 2520* 27720

%e 24 | 720 5040* 55440* 720720*

%e ...

%t (* Load b-file from A002182 *)

%t With[{s = Import["b002182.txt","Data"][[All,-1]]}, Array[#/Product[Prime@ i, {i, PrimeNu[#]}] &@ s[[#]] &, 62]]

%Y Cf. A002110, A002182, A108602, A301414.

%K nonn

%O 1,3

%A _Michael De Vlieger_, Mar 30 2018