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A359929 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).

%I A359929 #10 Apr 01 2023 13:29:05
%S A359929 12,18,24,18,36,20,40,12,24,36,48,48,54,45,50,60,18,36,54,72,28,56,40,
%T A359929 80,24,48,72,96,98,90,84,75,54,96,108,63,60,90,120,50,100,12,24,36,48,
%U A359929 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 A359929 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 A359929 Michael De Vlieger, <a href="/A359929/b359929.txt">Table of n, a(n) for n = 1..14675</a> (rows n = 1..3000, flattened)
%H A359929 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 A359929 Row lengths are in A359382.
%e A359929 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 A359929    n   b(n)  row n of this sequence
%e A359929   ---------------------------------
%e A359929    1    18   12;
%e A359929    2    24   18;
%e A359929    3    36   24;
%e A359929    4    48   18, 36;
%e A359929    5    50   20, 40;
%e A359929    6    54   12, 24, 36, 48;
%e A359929   ...
%e A359929    8    75   45;
%e A359929   ...
%e A359929   18   135   75;
%e A359929   ...
%e A359929   23   162   12, 24, 36, 48, 72, 96, 108, 144;
%e A359929   ...
%e A359929   56   375   45, 135, 225;
%e A359929   57   378   84, 168, 252, 294, 336;
%e A359929   58   384   18, 36, 54, 72, 108, 144, 162, 216, 288, 324
%t A359929 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A359929 s = Select[Range[2^7], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
%t A359929 t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@
%t A359929       {#, FactorInteger[#][[All, 1]]} &];
%t A359929 Flatten@ Map[Function[{n, k},
%t A359929     Select[TakeWhile[s, # < n &],
%t A359929       And[rad[#] == k, ! Divisible[n, #]] &]] @@ {#, rad[#]} &, t]
%Y A359929 Cf. A007947, A126706, A355432, A359382, A360768.
%K A359929 nonn,tabf
%O A359929 1,1
%A A359929 _Michael De Vlieger_, Mar 29 2023