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A225640 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. 14
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

In this array the maximization of LCM starts from partition {k} of k, instead of partition {1+1+...+1} as in A225630.

LINKS

Table of n, a(n) for n=0..77.

Index entries for sequences related to lcm's

EXAMPLE

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, ...

...

PROG

(Scheme):

(define (A225640 n) (A225640bi (A025581 n) (A002262 n)))

(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))))))))

CROSSREFS

Transpose: A225641.

Cf. A225642, A225644, A001477 (row 0), A225646 (row 1).

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.

Sequence in context: A186807 A114282 A112739 * A194543 A287920 A027293

Adjacent sequences:  A225637 A225638 A225639 * A225641 A225642 A225643

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 14 2013

STATUS

approved

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Last modified May 19 13:39 EDT 2019. Contains 323393 sequences. (Running on oeis4.)