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A286102
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Square array A(n,k) read by antidiagonals: A(n,k) = T(lcm(n,k), gcd(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table.
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6
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1, 3, 3, 6, 5, 6, 10, 21, 21, 10, 15, 14, 13, 14, 15, 21, 55, 78, 78, 55, 21, 28, 27, 120, 25, 120, 27, 28, 36, 105, 34, 210, 210, 34, 105, 36, 45, 44, 231, 90, 41, 90, 231, 44, 45, 55, 171, 300, 406, 465, 465, 406, 300, 171, 55, 66, 65, 64, 63, 630, 61, 630, 63, 64, 65, 66, 78, 253, 465, 666, 820, 903, 903, 820, 666, 465, 253, 78, 91, 90, 561, 230, 1035, 324, 85, 324, 1035, 230, 561, 90, 91
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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A(n,k) = T(lcm(n,k), gcd(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.
A(n,k) = A(k,n), or equivalently, a(A038722(n)) = a(n). [Array is symmetric.]
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EXAMPLE
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The top left 12 X 12 corner of the array:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78
3, 5, 21, 14, 55, 27, 105, 44, 171, 65, 253, 90
6, 21, 13, 78, 120, 34, 231, 300, 64, 465, 561, 103
10, 14, 78, 25, 210, 90, 406, 63, 666, 230, 990, 117
15, 55, 120, 210, 41, 465, 630, 820, 1035, 101, 1540, 1830
21, 27, 34, 90, 465, 61, 903, 324, 208, 495, 2211, 148
28, 105, 231, 406, 630, 903, 85, 1596, 2016, 2485, 3003, 3570
36, 44, 300, 63, 820, 324, 1596, 113, 2628, 860, 3916, 375
45, 171, 64, 666, 1035, 208, 2016, 2628, 145, 4095, 4950, 739
55, 65, 465, 230, 101, 495, 2485, 860, 4095, 181, 6105, 1890
66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 6105, 221, 8778
78, 90, 103, 117, 1830, 148, 3570, 375, 739, 1890, 8778, 265
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PROG
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(Scheme)
(define (A286102bi row col) (A000027bi (lcm row col) (gcd row col)))
(define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))
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CROSSREFS
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Cf. A000027, A003989, A003990, A003991, A038722, A285722, A285732, A286098, A286099, A286101, A285724.
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KEYWORD
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AUTHOR
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STATUS
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approved
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