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A304572
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Triangle read by rows: T(n,k) = 1 if k does not divide n^e, positive nonzero integers, and gcd(n,k) > 1.
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2
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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
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OFFSET
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1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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;
...
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MATHEMATICA
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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 *)
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PROG
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(PARI) T(n, k) = {my(r=vecprod(factor(k)[, 1])); n%r && gcd(n, k)<>1} \\ Andrew Howroyd, Nov 08 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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