A330541 -id:A330541 - cp's OEIS frontend

A330542 Maximum value in n-th row of A330541.

2, 6, 12, 30, 60, 120, 252, 504, 504, 504, 504, 2730, 16380, 32760, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 131040, 131040, 131040, 131040, 171864, 171864, 171864, 171864, 1919190, 11515140, 69090840

Offset: 2

Peter Kagey, Dec 17 2019

nonn

This sequence is weakly increasing.

Peter Kagey, Table of n, a(n) for n = 2..1000

A330590 Triangle read by rows: T(n,k) is the number of positive integers m dividing x^n - x^k for all integers x, 0 < k < n.

Original entry on oeis.org

2, 4, 2, 2, 6, 2, 8, 2, 8, 2, 2, 12, 2, 8, 2, 8, 2, 16, 2, 8, 2, 2, 18, 2, 20, 2, 8, 2, 8, 2, 24, 2, 20, 2, 8, 2, 2, 12, 2, 24, 2, 20, 2, 8, 2, 8, 2, 16, 2, 24, 2, 20, 2, 8, 2, 2, 12, 2, 20, 2, 24, 2, 20, 2, 8, 2, 32, 2, 16, 2, 24, 2, 24, 2, 20, 2, 8, 2, 2, 72

Offset: 2

Peter Kagey, Dec 18 2019

			Table begins:
  n\k| 1   2   3   4   5   6   7   8   9  10  11
  ---+-------------------------------------------------
   2 | 2;
   3 | 4,  2;
   4 | 2,  6,  2;
   5 | 8,  2,  8,  2;
   6 | 2, 12,  2,  8,  2;
   7 | 8,  2, 16,  2,  8,  2;
   8 | 2, 18,  2, 20,  2,  8,  2;
   9 | 8,  2, 24,  2, 20,  2,  8,  2;
  10 | 2, 12,  2, 24,  2, 20,  2,  8,  2;
  11 | 8,  2, 16,  2, 24,  2, 20,  2,  8,  2;
  12 | 2, 12,  2, 20,  2, 24,  2, 20,  2,  8,  2.
For n=4 and k=2, the sequence x^4 - x^2 evaluated on the positive (equivalently, negative) integers is 0,12,72,240,600,1260,2352,4032,6480,9900,... and all terms are divisible by the following T(4,2) = 6 positive integers: 1, 2, 3, 4, 6, and 12.

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

Cf. A000005, A330541.

T(n,k) = A000005(A330541(n,k)).

Conjecture: T(n,1) = 2^A067513(n-1).

cp's OEIS Frontend

A330542 Maximum value in n-th row of A330541.

Views

Author

Keywords

Comments

Links

A330590 Triangle read by rows: T(n,k) is the number of positive integers m dividing x^n - x^k for all integers x, 0 < k < n.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula