A349317 Triangle T(n,k): T(n,k) = 1 if gcd(n, k) > 1, else 0.

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

Cf. A000010, A051953, A054521, A067392, A066570.

Sequence in context: A212126 A144605 A349297 * A154103 A116178 A028999

Adjacent sequences: A349314 A349315 A349316 * A349318 A349319 A349320

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, Nov 14 2021

Status

approved