This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286146 #18 Mar 21 2025 18:28:06 %S A286146 1,2,5,4,16,13,7,12,67,25,11,46,106,191,41,16,23,31,80,436,61,22,92, %T A286146 211,379,596,862,85,29,38,277,59,781,302,1541,113,37,154,58,631,991, %U A286146 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 A286146 Lower triangular region of square array A286101. %H A286146 Antti Karttunen, <a href="/A286146/b286146.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of triangle</a> %F A286146 As a triangle (with n >= 1, 1 <= k <= n): %F A286146 T(n,k) = (1/2)*(2 + ((gcd(n,k)+lcm(n,k))^2) - gcd(n,k) - 3*lcm(n,k)). %e A286146 The first twelve rows of the triangle: %e A286146 1, %e A286146 2, 5, %e A286146 4, 16, 13, %e A286146 7, 12, 67, 25, %e A286146 11, 46, 106, 191, 41, %e A286146 16, 23, 31, 80, 436, 61, %e A286146 22, 92, 211, 379, 596, 862, 85, %e A286146 29, 38, 277, 59, 781, 302, 1541, 113, %e A286146 37, 154, 58, 631, 991, 193, 1954, 2557, 145, %e A286146 46, 57, 436, 212, 96, 467, 2416, 822, 4006, 181, %e A286146 56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996, 221, %e A286146 67, 80, 94, 109, 1771, 142, 3487, 355, 706, 1832, 8647, 265 %e A286146 ---------------------------------------------------------------- %e A286146 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 A286146 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 A286146 For T(12,1) we have gcd(12,1) = 1 and lcm(12,1) = 12, thus T(12,1) = T(4,3) = 67. %e A286146 For T(12,2) we have gcd(12,2) = 2 and lcm(12,1) = 12, thus T(12,1) = T(6,4) = 80. %e A286146 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 A286146 (Scheme) (define (A286146 n) (A286101bi (A002024 n) (A002260 n))) ;; For A286101bi see A286101. %o A286146 (Python) %o A286146 from sympy import lcm, gcd %o A286146 def t(n, k): return (2 + ((gcd(n, k) + lcm(n, k))**2) - gcd(n, k) - 3*lcm(n, k))/2 %o A286146 for n in range(1, 21): print([t(n, k) for k in range(1, n + 1)]) # _Indranil Ghosh_, May 11 2017 %Y A286146 Cf. A286101. %Y A286146 Cf. A286148 (same triangle reversed). %Y A286146 Cf. A000124 (the left edge), A001844 (the right edge). %K A286146 nonn,tabl %O A286146 1,2 %A A286146 _Antti Karttunen_, May 06 2017