A304571 Triangle read by rows: T(n,k) = 1 if gcd(k,n) > 1 and n mod k != 0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

T(n,k) = 1 iff both A051731(n,k) = 0 and A054521(n,k) = 0; T(n,k) = 0 otherwise.

This sequence contains 1 where 1 appears in row n of A304570 or A304572.

Row n of A133995 contains indices of 1 in this sequence.

A045763(n) = total of row n in this sequence.

Row p for p prime begins and ends with 1, but otherwise contains zeros; it is equivalent to row p of A051731.

Row n for n such that omega(n) = 1 contains only zeros; all other rows have at least one 1.

T(n,k) = 0 for k prime.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150)

Michael De Vlieger, Image of rows 1 <= n <= 2310

Example

Table begins:
0;
0, 0;
0, 0, 0;
0, 0, 0, 0;
0, 0, 0, 0, 0;
0, 0, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 1, 0, 1, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,;
...

Mathematica

Table[Array[Boole@ Nor[Mod[n, #] == 0, GCD[n, #] == 1] &, n], {n, 13}] // Flatten
(* Second program: extended data in rows from PNG image above: first, download the PNG and save it as "a304571.png", provides 2669205 terms: *)
MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304571.png", "PNG"]] (* Michael De Vlieger, Jul 02 2018 *)

Prog

(PARI) T(n, k) = {gcd(k, n)<>1 && n%k} \\ Andrew Howroyd, Nov 08 2018

Crossrefs

Cf. A045763, A051731, A054521, A133995, A304570, A304572.

Sequence in context: A011733 A297045 A304570 * A181838 A181837 A185709

Adjacent sequences: A304568 A304569 A304570 * A304572 A304573 A304574

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, May 23 2018

Status

approved