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%I #12 Nov 09 2018 07:28:30
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
%N Triangle read by rows: T(n,k) = 1 if k does not divide n^e, positive nonzero integers, and gcd(n,k) > 1.
%C T(n,k) = 1 iff both A304569(n,k) = 0 and A054521(n,k) = 0; T(n,k) = 0 otherwise.
%C This sequence contains 1 where 1 appears in row n of A304571 but not A304569.
%C Row n of A272619 contains indices of 1 in this sequence.
%C A243823(n) = total of row n in this sequence.
%C Rows n for n prime and n <= 6 contain only zeros; all other rows have at least one 1.
%C T(n,k) = 0 for k prime.
%H Michael De Vlieger, <a href="/A304572/b304572.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150)
%H Michael De Vlieger, <a href="/A304572/a304572.png">Image of rows 1 <= n <= 2310</a>
%e Table begins:
%e 0;
%e 0, 0;
%e 0, 0, 0;
%e 0, 0, 0, 0;
%e 0, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 1, 0, 0;
%e 0, 0, 0, 0, 0, 1, 0, 0, 0;
%e 0, 0, 0, 0, 0, 1, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0;
%e ...
%t Table[Array[Boole[And[PowerMod[n, Floor@ Log2@ n, #] != 0, GCD[n, #] > 1]] &, n], {n, 13}] // Flatten
%t (* Second program: extended data in rows from PNG image above: first, download the PNG and save it as "a304572.png", provides 2669205 terms: *)
%t MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304572.png", "PNG"]] (* _Michael De Vlieger_, Jul 02 2018 *)
%o (PARI) T(n,k) = {my(r=vecprod(factor(k)[,1])); n%r && gcd(n,k)<>1} \\ _Andrew Howroyd_, Nov 08 2018
%Y Cf. A054521, A243823, A272619, A304569, A304571.
%K nonn,easy,tabl
%O 1
%A _Michael De Vlieger_, May 23 2018
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