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A301413 a(n) = A002182(n)/A002110(A108602(n)).

%I A301413 #15 Oct 12 2023 01:53:26
%S A301413 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 A301413 24,36,48,72,96,120,144,216,240,288,24,36,48,72,96,120,144,216,240,
%U A301413 288,360,480,576,720,1080,72,1440,120,144,216,240,288,360,480,576
%N A301413 a(n) = A002182(n)/A002110(A108602(n)).
%C A301413 This sequence appears in Siano paper, page 5 of 12, as the "variable part" v. - _Michael De Vlieger_, Oct 11 2023
%H A301413 Michael De Vlieger, <a href="/A301413/b301413.txt">Table of n, a(n) for n = 1..10000</a>
%H A301413 Michael De Vlieger, <a href="http://vincico.com/proof/A301414.html">On a graph of highly composite numbers</a>
%H A301413 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.html">Highly composite numbers</a>
%H A301413 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 A301413 a(n) = A002182(n)/A007947(A002182(n)).
%e A301413 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 A301413         0  1   2    3     4       5       6 ...
%e A301413       +------------------------------------
%e A301413     1 | 1* 2*  6*
%e A301413     2 |    4  12*  60*
%e A301413     4 |       24  120*  840
%e A301413     6 |       36  180  1260
%e A301413     8 |       48  240  1680
%e A301413    12 |           360* 2520*  27720
%e A301413    24 |           720  5040*  55440* 720720*
%e A301413    ...
%t A301413 (* Load b-file from A002182 *)
%t A301413 With[{s = Import["b002182.txt","Data"][[All,-1]]}, Array[#/Product[Prime@ i, {i, PrimeNu[#]}] &@ s[[#]] &, 62]]
%Y A301413 Cf. A002110, A002182, A108602, A301414.
%K A301413 nonn
%O A301413 1,3
%A A301413 _Michael De Vlieger_, Mar 30 2018