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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.

%I A286102 #12 Feb 16 2025 08:33:44
%S A286102 1,3,3,6,5,6,10,21,21,10,15,14,13,14,15,21,55,78,78,55,21,28,27,120,
%T A286102 25,120,27,28,36,105,34,210,210,34,105,36,45,44,231,90,41,90,231,44,
%U A286102 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
%N 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.
%C A286102 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 A286102 Antti Karttunen, <a href="/A286102/b286102.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array</a>
%H A286102 MathWorld, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286102 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.
%F A286102 A(n,k) = A(k,n), or equivalently, a(A038722(n)) = a(n). [Array is symmetric.]
%e A286102 The top left 12 X 12 corner of the array:
%e A286102    1,   3,   6,  10,   15,   21,   28,   36,   45,   55,   66,   78
%e A286102    3,   5,  21,  14,   55,   27,  105,   44,  171,   65,  253,   90
%e A286102    6,  21,  13,  78,  120,   34,  231,  300,   64,  465,  561,  103
%e A286102   10,  14,  78,  25,  210,   90,  406,   63,  666,  230,  990,  117
%e A286102   15,  55, 120, 210,   41,  465,  630,  820, 1035,  101, 1540, 1830
%e A286102   21,  27,  34,  90,  465,   61,  903,  324,  208,  495, 2211,  148
%e A286102   28, 105, 231, 406,  630,  903,   85, 1596, 2016, 2485, 3003, 3570
%e A286102   36,  44, 300,  63,  820,  324, 1596,  113, 2628,  860, 3916,  375
%e A286102   45, 171,  64, 666, 1035,  208, 2016, 2628,  145, 4095, 4950,  739
%e A286102   55,  65, 465, 230,  101,  495, 2485,  860, 4095,  181, 6105, 1890
%e A286102   66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 6105,  221, 8778
%e A286102   78,  90, 103, 117, 1830,  148, 3570,  375,  739, 1890, 8778,  265
%o A286102 (Scheme)
%o A286102 (define (A286102 n) (A286102bi (A002260 n) (A004736 n)))
%o A286102 (define (A286102bi row col) (A000027bi (lcm row col) (gcd row col)))
%o A286102 (define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))
%Y A286102 Cf. A000027, A003989, A003990, A003991, A038722, A285722, A285732, A286098, A286099, A286101, A285724.
%Y A286102 Cf. A000217 (row 1 and column 1), A001844 (main diagonal).
%K A286102 nonn,tabl
%O A286102 1,2
%A A286102 _Antti Karttunen_, May 03 2017