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A376611
Irregular triangle read by rows: T(n,k) is the largest divisor of binomial(n,k) which is less than n, with 0 <= k <= n.
2
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 5, 5, 5, 3, 1, 1, 1, 3, 5, 5, 3, 1, 1, 1, 4, 7, 7, 7, 7, 7, 4, 1, 1, 3, 6, 7, 7, 7, 7, 6, 3, 1, 1, 5, 9, 8, 7, 9, 7, 8, 9, 5, 1, 1, 1, 5, 5, 10, 7, 7, 10, 5, 5, 1, 1, 1, 6, 11, 11, 11, 11, 11, 11, 11, 11, 11, 6, 1
OFFSET
2,9
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B23.
LINKS
Stefano Spezia, Table of n, a(n) for n = 2..5251 (first 100 rows of the triangle)
EXAMPLE
The irregular triangle begins as:
1, 1, 1;
1, 1, 1, 1;
1, 2, 3, 2, 1;
1, 1, 2, 2, 1, 1;
1, 3, 5, 5, 5, 3, 1;
1, 1, 3, 5, 5, 3, 1, 1;
1, 4, 7, 7, 7, 7, 7, 4, 1;
1, 3, 6, 7, 7, 7, 7, 6, 3, 1;
1, 5, 9, 8, 7, 9, 7, 8, 9, 5, 1;
1, 1, 5, 5, 10, 7, 7, 10, 5, 5, 1, 1;
...
MATHEMATICA
T[n_, k_]:=Max[Select[Divisors[Binomial[n, k]], #<n &]]; Table[T[n, k], {n, 2, 12}, {k, 0, n}]//Flatten
CROSSREFS
Cf. A000012 (n=k or k=0), A007318, A027750, A032742 (k=1).
Cf. A376612 (less than k).
Sequence in context: A039735 A283761 A171457 * A129385 A217983 A096626
KEYWORD
nonn,look,tabf
AUTHOR
Stefano Spezia, Sep 29 2024
STATUS
approved