login
A349317
Triangle T(n,k): T(n,k) = 1 if gcd(n, k) > 1, else 0.
1
0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
Characteristic function of k in the cototient of n, i.e., of A169582: a(A169582(n)) = 1; a(A169581(n)) = 0.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened)
Michael De Vlieger, Bitmap of 256 rows enlarged 4X, with 1's in black and 0's in white.
Michael De Vlieger, Bitmap of 4096 rows with 1's in black and 0's in white.
FORMULA
Row sums are in A051953 = n - A000010(n).
A067392 = Sum of k*T(n,k).
A066570 = Product of k in row n such that T(n,k)=1
Inverse of A054521 = S(n,k); T(n,k) = 1 - S(n,k).
EXAMPLE
Table T(n,k) for 1 <= n <= 16, replacing 0 with "." for clarity:
1: .
2: . 1
3: . . 1
4: . 1 . 1
5: . . . . 1
6: . 1 1 1 . 1
7: . . . . . . 1
8: . 1 . 1 . 1 . 1
9: . . 1 . . 1 . . 1
10: . 1 . 1 1 1 . 1 . 1
11: . . . . . . . . . . 1
12: . 1 1 1 . 1 . 1 1 1 . 1
13: . . . . . . . . . . . . 1
14: . 1 . 1 . 1 1 1 . 1 . 1 . 1
15: . . 1 . 1 1 . . 1 1 . 1 . . 1
16: . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1
---------------------------------------------------
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
MATHEMATICA
Table[Boole[GCD[n, k] > 1], {n, 13}, {k, n}] // Flatten
(* Generate up to 4096 rows = 8390656 terms from data stored in the bitmap: *)
With[{rows = 150, s = ImageData[Import["https://oeis.org/A349317/a349317_1.png"]]}, Array[s[[#, 1 ;; #]] /. {0. -> 1, 1. -> 0} &, rows]] (* Michael De Vlieger, Dec 08 2021 *)
CROSSREFS
KEYWORD
nonn,easy,tabl
AUTHOR
Michael De Vlieger, Nov 14 2021
STATUS
approved