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A330541
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Triangle read by rows: T(n,k) = gcd {x^n - x^k : x is an integer}, 0 < k < n.
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3
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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
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OFFSET
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2,1
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COMMENTS
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All diagonals are weakly increasing, T(n,k) divides T(n+1,k+1), and the m-th diagonal converges to A079612(m).
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).
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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