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
KEYWORD
nonn,tabf
AUTHOR
Michael De Vlieger, Mar 29 2023
STATUS
approved