%I #15 Dec 07 2019 12:18:29

%S 1,2,5,4,16,13,7,12,67,25,11,46,106,191,41,16,23,31,80,436,61,22,92,

%T 211,379,596,862,85,29,38,277,59,781,302,1541,113,37,154,58,631,991,

%U 193,1954,2557,145,46,57,436,212,96,467,2416,822,4006,181,56,232,529,947,1486,2146,2927,3829,4852,5996,221,67,80,94,109,1771,142,3487,355,706,1832,8647

%N Lower triangular region of square array A286101.

%H Antti Karttunen, <a href="/A286146/b286146.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of triangle</a>

%F As a triangle (with n >= 1, 1 <= k <= n):

%F T(n,k) = (1/2)*(2 + ((gcd(n,k)+lcm(n,k))^2) - gcd(n,k) - 3*lcm(n,k)).

%e The first twelve rows of the triangle:

%e 1,

%e 2, 5,

%e 4, 16, 13,

%e 7, 12, 67, 25,

%e 11, 46, 106, 191, 41,

%e 16, 23, 31, 80, 436, 61,

%e 22, 92, 211, 379, 596, 862, 85,

%e 29, 38, 277, 59, 781, 302, 1541, 113,

%e 37, 154, 58, 631, 991, 193, 1954, 2557, 145,

%e 46, 57, 436, 212, 96, 467, 2416, 822, 4006, 181,

%e 56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996, 221,

%e 67, 80, 94, 109, 1771, 142, 3487, 355, 706, 1832, 8647, 265

%e ----------------------------------------------------------------

%e For T(4,3) we have gcd(4,3) = 1 and lcm(4,3) = 12, thus T(4,3) = (1/2)*(2 + (12+1)^2 - 1 - 3*12) = 67.

%e For T(6,4) we have gcd(6,4) = 2 and lcm(6,4) = 12, thus T(6,4) = (1/2)*(2 + (12+2)^2 - 2 - 3*12) = 80.

%e For T(12,1) we have gcd(12,1) = 1 and lcm(12,1) = 12, thus T(12,1) = T(4,3) = 67.

%e For T(12,2) we have gcd(12,2) = 2 and lcm(12,1) = 12, thus T(12,1) = T(6,4) = 80.

%e For T(12,8) we have gcd(12,8) = 4 and lcm(12,8) = 24, thus T(12,8) = (1/2)*(2 + (24+4)^2 - 4 - 3*24) = 355.

%o (Scheme) (define (A286146 n) (A286101bi (A002024 n) (A002260 n))) ;; For A286101bi see A286101.

%o (Python)

%o from sympy import lcm, gcd

%o def t(n, k): return (2 + ((gcd(n, k) + lcm(n, k))**2) - gcd(n, k) - 3*lcm(n, k))/2

%o for n in range(1, 21): print [t(n, k) for k in range(1, n + 1)] # _Indranil Ghosh_, May 11 2017

%Y Cf. A286101.

%Y Cf. A286148 (same triangle reversed).

%Y Cf. A000124 (the left edge), A001844 (the right edge).

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, May 06 2017