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Triangle read by rows: T(n,k) = 1 if k | n^e with e >= 0, otherwise T(n,k) = 0 (1 <= k <= n).
3

%I #14 Nov 08 2018 19:00:03

%S 1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,1,0,0,

%T 0,1,1,0,1,0,0,0,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,

%U 1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0

%N Triangle read by rows: T(n,k) = 1 if k | n^e with e >= 0, otherwise T(n,k) = 0 (1 <= k <= n).

%C Row n of A162306 contains indices of 1 in this sequence.

%C A010846(n) = total of row n in this sequence.

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

%C Row n for n such that omega(n) = 1 is the same as row n of A051731.

%C All other rows have additional 1s at positions in row n of A272618.

%H Michael De Vlieger, <a href="/A304569/b304569.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150)

%H Michael De Vlieger, <a href="/A304569/a304569.png">Image of rows 1 <= n <= 2310</a>,

%e Table begins:

%e 1;

%e 1, 1;

%e 1, 0, 1;

%e 1, 1, 0, 1;

%e 1, 0, 0, 0, 1;

%e 1, 1, 1, 1, 0, 1;

%e 1, 0, 0, 0, 0, 0, 1;

%e 1, 1, 0, 1, 0, 0, 0, 1;

%e 1, 0, 1, 0, 0, 0, 0, 0, 1;

%e 1, 1, 0, 1, 1, 0, 0, 1, 0, 1;

%e ...

%t Table[Array[Boole[PowerMod[n, Floor@ Log2@ n, #] == 0] &, n], {n, 13}] // Flatten

%t (* Second program: extended data in rows from PNG image above: first, download the PNG and save it as "a304569.png", provides 2669205 terms: *)

%t MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304569.png", "PNG"]] (* _Michael De Vlieger_, May 23 2018 *)

%o (PARI) T(n, k) = {if (k==1, 1, my (f = factor(k)); sum(k=1, #f~, n % f[k,1]) == 0);}

%o tabl(nn) = {for(n=1, nn, for(k=1, n, print1(T(n,k), ", "); ); print(); ); }; \\ _Michel Marcus_, May 23 2018

%Y Cf. A010846, A051731, A162306, A243103, A244974, A272618.

%K nonn,easy,tabl

%O 1

%A _Michael De Vlieger_, May 15 2018