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A304572
Triangle read by rows: T(n,k) = 1 if k does not divide n^e, positive nonzero integers, and gcd(n,k) > 1.
2
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
KEYWORD
nonn,easy,tabl
AUTHOR
Michael De Vlieger, May 23 2018
STATUS
approved