A330590 - OEIS

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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.

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: A368435 A058384 A255671 * A055097 A258751 A280233

Adjacent sequences: A330587 A330588 A330589 * A330591 A330592 A330593

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Dec 18 2019

STATUS

approved