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%I #10 Apr 01 2023 13:29:05
%S 12,18,24,18,36,20,40,12,24,36,48,48,54,45,50,60,18,36,54,72,28,56,40,
%T 80,24,48,72,96,98,90,84,75,54,96,108,63,60,90,120,50,100,12,24,36,48,
%U 72,96,108,144,126,120,150,147,18,36,54,72,108,144,162,56,112,132,80,160,48,96,144,162,192,98,196
%N Irregular triangle read by rows, where row n lists k < t such that rad(k) = rad(t) but k does not divide t, where t = A360768(n) and rad(k) = A007947(k).
%H Michael De Vlieger, <a href="/A359929/b359929.txt">Table of n, a(n) for n = 1..14675</a> (rows n = 1..3000, flattened)
%H Michael De Vlieger, <a href="/A359929/a359929.png">Plot (k, t) at (x, -y)</a>, where k = A126706(i) and t = A360768(j) for i = 1..48 and j = 1..108, showing k in dark blue, t in dark red, and for t and nondivisor k such that rad(k) = rad(t), we highlight in large black dots. This sequence counts the number of black dots in row n.
%F Row lengths are in A359382.
%e Table of some of the first rows of the sequence, showing both even and odd b(n) = A360768(n) with both a single and multiple terms in the row:
%e n b(n) row n of this sequence
%e ---------------------------------
%e 1 18 12;
%e 2 24 18;
%e 3 36 24;
%e 4 48 18, 36;
%e 5 50 20, 40;
%e 6 54 12, 24, 36, 48;
%e ...
%e 8 75 45;
%e ...
%e 18 135 75;
%e ...
%e 23 162 12, 24, 36, 48, 72, 96, 108, 144;
%e ...
%e 56 375 45, 135, 225;
%e 57 378 84, 168, 252, 294, 336;
%e 58 384 18, 36, 54, 72, 108, 144, 162, 216, 288, 324
%t rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t s = Select[Range[2^7], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
%t t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@
%t {#, FactorInteger[#][[All, 1]]} &];
%t Flatten@ Map[Function[{n, k},
%t Select[TakeWhile[s, # < n &],
%t And[rad[#] == k, ! Divisible[n, #]] &]] @@ {#, rad[#]} &, t]
%Y Cf. A007947, A126706, A355432, A359382, A360768.
%K nonn,tabf
%O 1,1
%A _Michael De Vlieger_, Mar 29 2023
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