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

1,1

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.

Formula

Row lengths are in A359382.

Example

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

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]

Crossrefs

Cf. A007947, A126706, A355432, A359382, A360768.

Sequence in context: A031207 A107794 A280014 * A162151 A056773 A297925

Adjacent sequences: A359926 A359927 A359928 * A359930 A359931 A359932

Keyword

nonn,tabf

Author

Michael De Vlieger, Mar 29 2023

Status

approved