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).
12, 18, 24, 18, 36, 20, 40, 12, 24, 36, 48, 48, 54, 45, 50, 60, 18, 36, 54, 72, 28, 56, 40, 80, 24, 48, 72, 96, 98, 90, 84, 75, 54, 96, 108, 63, 60, 90, 120, 50, 100, 12, 24, 36, 48, 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
Offset: 1
Examples
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: n b(n) row n of this sequence --------------------------------- 1 18 12; 2 24 18; 3 36 24; 4 48 18, 36; 5 50 20, 40; 6 54 12, 24, 36, 48; ... 8 75 45; ... 18 135 75; ... 23 162 12, 24, 36, 48, 72, 96, 108, 144; ... 56 375 45, 135, 225; 57 378 84, 168, 252, 294, 336; 58 384 18, 36, 54, 72, 108, 144, 162, 216, 288, 324
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..14675 (rows n = 1..3000, flattened)
- Michael De Vlieger, Plot (k, t) at (x, -y), 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.
Programs
-
Mathematica
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; s = Select[Range[2^7], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]; t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]; Flatten@ Map[Function[{n, k}, Select[TakeWhile[s, # < n &], And[rad[#] == k, ! Divisible[n, #]] &]] @@ {#, rad[#]} &, t]
Formula
Row lengths are in A359382.