A304572 Triangle read by rows: T(n,k) = 1 if k does not divide n^e, positive nonzero integers, and gcd(n,k) > 1.

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

Offset

1

Comments

T(n,k) = 1 iff both A304569(n,k) = 0 and A054521(n,k) = 0; T(n,k) = 0 otherwise.

This sequence contains 1 where 1 appears in row n of A304571 but not A304569.

Row n of A272619 contains indices of 1 in this sequence.

A243823(n) = total of row n in this sequence.

Rows n for n prime and n <= 6 contain 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, 0, 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, 0, 0, 1, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0;
...

Mathematica

Table[Array[Boole[And[PowerMod[n, Floor@ Log2@ 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 "a304572.png", provides 2669205 terms: *)
MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304572.png", "PNG"]] (* Michael De Vlieger, Jul 02 2018 *)

Prog

(PARI) T(n, k) = {my(r=vecprod(factor(k)[, 1])); n%r && gcd(n, k)<>1} \\ Andrew Howroyd, Nov 08 2018

Crossrefs

Cf. A054521, A243823, A272619, A304569, A304571.

Sequence in context: A072769 A353625 A322438 * A070204 A011745 A011744

Adjacent sequences: A304569 A304570 A304571 * A304573 A304574 A304575

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, May 23 2018

Status

approved