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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.

%I A285724 #13 Feb 16 2025 08:33:44
%S A285724 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,
%T A285724 120,27,28,29,92,31,191,210,34,105,36,37,38,211,80,41,90,231,44,45,46,
%U A285724 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
%N 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.
%C A285724 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.
%H A285724 Antti Karttunen, <a href="/A285724/b285724.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array</a>
%H A285724 MathWorld, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A285724 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.
%F A285724 If n < k, A(n,k) = A286101(n,k), otherwise A(n,k) = A286102(n,k).
%e A285724 The top left 12 X 12 corner of the array:
%e A285724    1,   2,   4,   7,   11,   16,   22,   29,   37,   46,   56,   67
%e A285724    3,   5,  16,  12,   46,   23,   92,   38,  154,   57,  232,   80
%e A285724    6,  21,  13,  67,  106,   31,  211,  277,   58,  436,  529,   94
%e A285724   10,  14,  78,  25,  191,   80,  379,   59,  631,  212,  947,  109
%e A285724   15,  55, 120, 210,   41,  436,  596,  781,  991,   96, 1486, 1771
%e A285724   21,  27,  34,  90,  465,   61,  862,  302,  193,  467, 2146,  142
%e A285724   28, 105, 231, 406,  630,  903,   85, 1541, 1954, 2416, 2927, 3487
%e A285724   36,  44, 300,  63,  820,  324, 1596,  113, 2557,  822, 3829,  355
%e A285724   45, 171,  64, 666, 1035,  208, 2016, 2628,  145, 4006, 4852,  706
%e A285724   55,  65, 465, 230,  101,  495, 2485,  860, 4095,  181, 5996, 1832
%e A285724   66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 6105,  221, 8647
%e A285724   78,  90, 103, 117, 1830,  148, 3570,  375,  739, 1890, 8778,  265
%o A285724 (Scheme)
%o A285724 (define (A285724 n) (A285724bi (A002260 n) (A004736 n)))
%o A285724 (define (A285724bi row col) (if (> row col) (A000027bi (lcm row col) (gcd row col)) (A000027bi (gcd row col) (lcm row col))))
%o A285724 (define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))
%Y A285724 Cf. A000124 (row 1), A000217 (column 1), A001844 (main diagonal).
%Y A285724 Cf. A000027, A003989, A003990, A003991, A286101, A286102, A286155, A285722.
%K A285724 nonn,tabl
%O A285724 1,2
%A A285724 _Antti Karttunen_, May 03 2017