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A286102
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.
6
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
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
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.]
EXAMPLE
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
PROG
(Scheme)
(define (A286102 n) (A286102bi (A002260 n) (A004736 n)))
(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)))
CROSSREFS
Cf. A000217 (row 1 and column 1), A001844 (main diagonal).
Sequence in context: A142149 A132119 A180681 * A023822 A318514 A355413
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved