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A285724
Square array read by descending antidiagonals: If n > k, A(n,k) = T(lcm(n,k), gcd(n,k)), otherwise A(n,k) = T(gcd(n,k), lcm(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table.
3
1, 2, 3, 4, 5, 6, 7, 16, 21, 10, 11, 12, 13, 14, 15, 16, 46, 67, 78, 55, 21, 22, 23, 106, 25, 120, 27, 28, 29, 92, 31, 191, 210, 34, 105, 36, 37, 38, 211, 80, 41, 90, 231, 44, 45, 46, 154, 277, 379, 436, 465, 406, 300, 171, 55, 56, 57, 58, 59, 596, 61, 630, 63, 64, 65, 66, 67, 232, 436, 631, 781, 862, 903, 820, 666, 465, 253, 78, 79, 80, 529, 212, 991, 302, 85, 324, 1035, 230, 561, 90, 91
OFFSET
1,2
COMMENTS
The array is read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
FORMULA
If n > k, A(n,k) = T(lcm(n,k),gcd(n,k)), otherwise A(n,k) = T(gcd(n,k),lcm(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table, that is, as a pairing function from N x N to N.
If n < k, A(n,k) = A286101(n,k), otherwise A(n,k) = A286102(n,k).
EXAMPLE
The top left 12 X 12 corner of the array:
1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67
3, 5, 16, 12, 46, 23, 92, 38, 154, 57, 232, 80
6, 21, 13, 67, 106, 31, 211, 277, 58, 436, 529, 94
10, 14, 78, 25, 191, 80, 379, 59, 631, 212, 947, 109
15, 55, 120, 210, 41, 436, 596, 781, 991, 96, 1486, 1771
21, 27, 34, 90, 465, 61, 862, 302, 193, 467, 2146, 142
28, 105, 231, 406, 630, 903, 85, 1541, 1954, 2416, 2927, 3487
36, 44, 300, 63, 820, 324, 1596, 113, 2557, 822, 3829, 355
45, 171, 64, 666, 1035, 208, 2016, 2628, 145, 4006, 4852, 706
55, 65, 465, 230, 101, 495, 2485, 860, 4095, 181, 5996, 1832
66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 6105, 221, 8647
78, 90, 103, 117, 1830, 148, 3570, 375, 739, 1890, 8778, 265
PROG
(Scheme)
(define (A285724 n) (A285724bi (A002260 n) (A004736 n)))
(define (A285724bi row col) (if (> row col) (A000027bi (lcm row col) (gcd row col)) (A000027bi (gcd row col) (lcm row col))))
(define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))
CROSSREFS
Cf. A000124 (row 1), A000217 (column 1), A001844 (main diagonal).
Sequence in context: A250045 A132028 A332535 * A193551 A277439 A069188
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved