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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
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
Sequence in context: A368435 A058384 A255671 * A055097 A258751 A280233
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Dec 18 2019
STATUS
approved