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A286101
Square array A(n,k) read by antidiagonals: A(n,k) = T(gcd(n,k), lcm(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table.
8
1, 2, 2, 4, 5, 4, 7, 16, 16, 7, 11, 12, 13, 12, 11, 16, 46, 67, 67, 46, 16, 22, 23, 106, 25, 106, 23, 22, 29, 92, 31, 191, 191, 31, 92, 29, 37, 38, 211, 80, 41, 80, 211, 38, 37, 46, 154, 277, 379, 436, 436, 379, 277, 154, 46, 56, 57, 58, 59, 596, 61, 596, 59, 58, 57, 56, 67, 232, 436, 631, 781, 862, 862, 781, 631, 436, 232, 67, 79, 80, 529, 212, 991, 302, 85, 302, 991, 212, 529, 80, 79
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(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.
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, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67
2, 5, 16, 12, 46, 23, 92, 38, 154, 57, 232, 80
4, 16, 13, 67, 106, 31, 211, 277, 58, 436, 529, 94
7, 12, 67, 25, 191, 80, 379, 59, 631, 212, 947, 109
11, 46, 106, 191, 41, 436, 596, 781, 991, 96, 1486, 1771
16, 23, 31, 80, 436, 61, 862, 302, 193, 467, 2146, 142
22, 92, 211, 379, 596, 862, 85, 1541, 1954, 2416, 2927, 3487
29, 38, 277, 59, 781, 302, 1541, 113, 2557, 822, 3829, 355
37, 154, 58, 631, 991, 193, 1954, 2557, 145, 4006, 4852, 706
46, 57, 436, 212, 96, 467, 2416, 822, 4006, 181, 5996, 1832
56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996, 221, 8647
67, 80, 94, 109, 1771, 142, 3487, 355, 706, 1832, 8647, 265
PROG
(Scheme)
(define (A286101 n) (A286101bi (A002260 n) (A004736 n)))
(define (A286101bi 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 and column 1), A001844 (main diagonal).
Sequence in context: A136099 A210597 A252836 * A072454 A115216 A208637
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 03 2017
STATUS
approved