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A304570
Triangle read by rows: T(n,k) = 1 if k | n^e with e > 1 and n mod k != 0, T(n,k) = 0 otherwise (1 <= k <= n).
3
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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1
COMMENTS
T(n,k) = 1 iff A051731(n,k) = 0 but A304569(n,k) = 1; T(n,k) = 0 otherwise. This sequence contains 1 where 1 appears in row n of A304569 but not in same row of A051731.
Row n of A272618 contains indices of 1 in this sequence.
A243822(n) = total of row n in this sequence.
Row n such that omega(n) = 1 contains zeros.
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, 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, 0, 0;
0, 0, 0, 1, 0, 0, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,;
...
MATHEMATICA
Table[Boole[And[PowerMod[n, Floor@ Log2@ n, #] == 0, Mod[n, #] > 0]], {n, 13}] // Flatten
(* Second program: extended data in rows from PNG image above: first, download the PNG and save it as "a304570.png", provides 2669205 terms: *)
MapIndexed[Take[#1, First@ #2] &, ImageData@ ColorNegate@ Import["a304570.png", "PNG"]] (* Michael De Vlieger, Jul 02 2018 *)
PROG
(PARI) T(n, k) = {my(r=vecprod(factor(k)[, 1])); n%k<>0 && n%r==0} \\ Andrew Howroyd, Nov 08 2018
CROSSREFS
KEYWORD
nonn,easy,tabl
AUTHOR
Michael De Vlieger, May 23 2018
EXTENSIONS
Name clarified by Andrew Howroyd, Nov 08 2018
STATUS
approved