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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

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

FORMULA

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

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

EXAMPLE

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.

CROSSREFS

Cf. A000005, A330541.

Sequence in context: A144049 A058384 A255671 * A055097 A258751 A280233

Adjacent sequences:  A330587 A330588 A330589 * A330591 A330592 A330593

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Dec 18 2019

STATUS

approved

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Last modified September 28 11:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)