A304569 Triangle read by rows: T(n,k) = 1 if k | n^e with e >= 0, otherwise T(n,k) = 0 (1 <= k <= n).

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

Offset

1

Comments

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

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

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

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

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

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:
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, 0, 1;
1, 0, 1, 0, 0, 0, 0, 0, 1;
1, 1, 0, 1, 1, 0, 0, 1, 0, 1;
...

Mathematica

Table[Array[Boole[PowerMod[n, Floor@ Log2@ n, #] == 0] &, n], {n, 13}] // Flatten
(* Second program: extended data in rows from PNG image above: first, download the PNG and save it as "a304569.png", provides 2669205 terms: *)
MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304569.png", "PNG"]] (* Michael De Vlieger, May 23 2018 *)

Prog

(PARI) T(n, k) = {if (k==1, 1, my (f = factor(k)); sum(k=1, #f~, n % f[k, 1]) == 0); }
tabl(nn) = {for(n=1, nn, for(k=1, n, print1(T(n, k), ", "); ); print(); ); }; \\ Michel Marcus, May 23 2018

Crossrefs

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

Sequence in context: A174854 A103994 A051731 * A135839 A071022 A155076

Adjacent sequences: A304566 A304567 A304568 * A304570 A304571 A304572

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, May 15 2018

Status

approved