Triangle of the least powerful number p such that p = i (mod n), or 0 if no such p exists.
1, 4, 1, 9, 1, 8, 4, 1, 0, 27, 25, 1, 32, 8, 4, 36, 1, 8, 9, 4, 125, 49, 1, 9, 108, 4, 243, 27, 16, 1, 0, 27, 4, 125, 0, 343, 9, 1, 128, 0, 4, 32, 0, 16, 8, 100, 1, 32, 243, 4, 25, 16, 27, 8, 9, 121, 1, 200, 25, 4, 16, 72, 128, 8, 9, 32, 36, 1, 0, 27, 4, 125, 0
1
For rows n > 1, the second term (for k = 1) in the row is always 1.
T. D. Noe, Plot of 100 rows of triangle
T. D. Noe, Table of 100 rows of triangle
(Mma) nn = 8; nMax = 10^nn; lst = {}; Do[lst = Join[lst, i^3 Range[Sqrt[nMax/i^3]]^2], {i, nMax^(1/3)}]; seq = Table[good = Transpose[Tally[Mod[lst, n]]][[1]]; Table[If[MemberQ[good, i], s = Select[lst, Mod[#, n] == i &, 1]; s[[1]], 0], {i, 0, n - 1}], {n, 12}]
Cf. A001694 (powerful), S000119, S000120.
nonn,tabl
T. D. Noe, Jul 04 2014