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A225640
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Array A(n,k) of iterated Landau-like functions, where on the row n=0 A(0,0)=1 and A(0,k>=1)=k, and the successive rows A(n,k) give a maximum value lcm(p1,p2,...,pj,A(n-1,k)) for all partitions {p1+p2+...+pj} of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
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14
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1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 6, 2, 1, 1, 5, 12, 6, 2, 1, 1, 6, 30, 12, 6, 2, 1, 1, 7, 30, 60, 12, 6, 2, 1, 1, 8, 84, 60, 60, 12, 6, 2, 1, 1, 9, 120, 420, 60, 60, 12, 6, 2, 1, 1, 10, 180, 840, 420, 60, 60, 12, 6, 2, 1, 1, 11, 210, 1260, 840, 420, 60, 60, 12, 6, 2, 1, 1
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OFFSET
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0,4
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COMMENTS
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In this array the maximization of LCM starts from partition {k} of k, instead of partition {1+1+...+1} as in A225630.
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LINKS
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EXAMPLE
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The top-left corner of the array:
1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
1, 1, 2, 6, 12, 30, 30, 84, 120, 180, 210, 330, 420, ...
1, 1, 2, 6, 12, 60, 60, 420, 840, 1260, 840, 4620, 4620, ...
1, 1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520, 13860, 13860, ...
1, 1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520, 27720, 27720, ...
...
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PROG
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(Scheme):
(define (A225640bi col row) (let ((maxlcm (list 0))) (let loop ((prevmaxlcm (max 1 col)) (stepsleft row)) (if (zero? stepsleft) prevmaxlcm (begin (gen_partitions col (lambda (p) (set-car! maxlcm (max (car maxlcm) (apply lcm (cons prevmaxlcm p)))))) (loop (car maxlcm) (- stepsleft 1)))))))
(define (gen_partitions m colfun) (let recurse ((m m) (b m) (n 0) (partition (list))) (cond ((zero? m) (colfun partition)) (else (let loop ((i 1)) (recurse (- m i) i (+ 1 n) (cons i partition)) (if (< i (min b m)) (loop (+ 1 i))))))))
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CROSSREFS
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Rows converge towards A003418 (main diagonal of this array).
See A225630 for a variant employing a similar process, but which uses 1 in column n as the initial seed for that column, instead of n.
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KEYWORD
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AUTHOR
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STATUS
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approved
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