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%I #9 May 16 2018 12:02:22
%S 1,2,4,12,24,48,144,720,1440,10080,30240,60480,302400,604800,6652800,
%T 19958400,259459200,518918400,3632428800,61751289600,185253868800,
%U 926269344000,17599117536000,35198235072000,809559406656000,1619118813312000,4857356439936000
%N Numbers k in A301413 such that k * A002110 (m) is in A002201.
%H Michael De Vlieger, <a href="/A301416/b301416.txt">Table of n, a(n) for n = 1..170</a>
%H Michael De Vlieger, <a href="/A301416/a301416.png">Plot m = a(x) * A002110(y) at (x,y) for m in A002201</a>, smallest 4096 terms m.
%e From _Michael De Vlieger_, May 14 2018: (Start)
%e Numbers m = A301416(x) * A002110(y) that are in A002201 are plotted below.
%e 1 2 3 4 5 6 7 ...
%e +-----------------------------------------------
%e 1 | 2
%e 2 | 6 12
%e 3 | 60 120 360
%e 4 | 2520 5040
%e 5 | 55440
%e 6 | 720720 1441440 4324320
%e ...
%e (End)
%t t = Import["b002201.txt", "Data"][[All, -1]]; (* Uses b-file at A002201 Alternatively, use this conversion of terms at A000705 to a 10^4 term dataset for A002201. Processing 10^4 terms will take a long time: *) t = With[{s = Import["b000705.txt", "Data"][[All, -1]]}, FoldList[Times, s]]; f[n_] := With[{d = FactorInteger@ n}, If[n == 1, {0}, ReplacePart[Table[0, {PrimePi[d[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, d]]]; Union@ Array[Times @@ MapIndexed[Prime[First@#2]^#1 &, #3] & @@ {#1, Boole[First@ #2 > 0] Length@ #2, DeleteCases[-1 + #2, 0] /. -1 -> 0} & @@ {t[[#]], f@ t[[#]]} &, Length@ t]
%Y Cf. A002110, A002201, A301413, A301414.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Apr 09 2018
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