A330541 Triangle read by rows: T(n,k) = gcd {x^n - x^k : x is an integer}, 0 < k < n.

2, 6, 2, 2, 12, 2, 30, 2, 24, 2, 2, 60, 2, 24, 2, 42, 2, 120, 2, 24, 2, 2, 252, 2, 240, 2, 24, 2, 30, 2, 504, 2, 240, 2, 24, 2, 2, 60, 2, 504, 2, 240, 2, 24, 2, 66, 2, 120, 2, 504, 2, 240, 2, 24, 2, 2, 132, 2, 240, 2, 504, 2, 240, 2, 24, 2

Offset

2,1

Comments

All diagonals are weakly increasing, T(n,k) divides T(n+1,k+1), and the m-th diagonal converges to A079612(m).

First column is A027760.

First value where T(n,k) < gcd(2^n - 2^k, 3^n - 3^k) is T(12,1) = 2 < 46.

Maximum value in the n-th row is given by A330542(n).

Links

Peter Kagey, Table of n, a(n) for n = 2..10012 (first 141 rows, flattened)

Mathematics Stack Exchange, Computing gcd {n^k - n^l : n in Z}.

Example

Table begins:
  n\k|  1    2    3    4    5    6    7    8   9  10 11
  ---+-------------------------------------------------
   2 |  2;
   3 |  6,   2;
   4 |  2,  12,   2;
   5 | 30,   2,  24,   2;
   6 |  2,  60,   2,  24,   2;
   7 | 42,   2, 120,   2,  24,   2;
   8 |  2, 252,   2, 240,   2,  24,   2;
   9 | 30,   2, 504,   2, 240,   2,  24,   2;
  10 |  2,  60,   2, 504,   2, 240,   2,  24,  2;
  11 | 66,   2, 120,   2, 504,   2, 240,   2, 24,  2;
  12 |  2, 132,   2, 240,   2, 504,   2, 240,  2, 24, 2.

Crossrefs

Cf. A027760, A079612, A330542.

Sequence in context: A347238 A171898 A378973 * A320575 A110218 A316259

Adjacent sequences: A330538 A330539 A330540 * A330542 A330543 A330544

Keyword

nonn,tabl

Author

Peter Kagey, Dec 17 2019

Status

approved