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 A256095 #17 Jan 21 2020 09:13:38
%S A256095 0,1,1,3,1,3,6,1,3,6,10,1,1,2,10,15,1,3,3,5,15,21,1,3,3,1,3,21,28,1,1,
%T A256095 2,2,1,7,28,36,1,3,6,2,3,3,4,36,45,1,3,3,5,15,3,1,9,45,55,1,1,1,5,5,1,
%U A256095 1,1,5,55,66,1,3,6,2,3,3,2,6,3,11,66,78,1,3,6,2,3,3,2,6,3,1,6,78,91,1,1,1,1,1,7,7,1,1,1,1,13,91,105,1,3,3,5,15,21,7,3,15,5,3,3,7,105
%N A256095 Triangle of greatest common divisors of two triangular numbers (A000217).
%H A256095 Robert Israel, <a href="/A256095/b256095.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)
%F A256095 T(n, m) = gcd(Tri(n), Tri(m)), 0 <= m <= n, with the triangular numbers Tri = A000217.
%F A256095 T(n, 0) = Tri(n) = T(n, n). T(n, 1) = 1, n >= 0.
%F A256095 Columns m=2: A144437(n-1), m=3: repeat(6, 2, 3, 3, 2, 6, 3, 1, 6, 6, 1, 3) (guess), m=4: repeat(10, 5, 1, 2, 2, 5, 5, 2, 2, 1, 5, 10, 2, 1, 1, 10, 10, 1, 1, 2) (guess), m=5 repeat(15, 3, 1, 3, 15, 5, 3, 3, 1, 15, 15, 1, 3, 3, 5) (guess), ...
%F A256095 From _Robert Israel_, Jan 21 2020: (Start) The guesses are correct. More generally, for each k>=1, T(n,k) is periodic in n with period 2*A000217(k) if k == 0 or 3 (mod 4), A000217(k) if k == 1 or 2 (mod 4). (End)
%e A256095 The triangle T(n, m) begins:
%e A256095 n\m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e A256095 0: 0
%e A256095 1: 1 1
%e A256095 2: 3 1 3
%e A256095 3: 6 1 3 6
%e A256095 4: 10 1 1 2 10
%e A256095 5: 15 1 3 3 5 15
%e A256095 6: 21 1 3 3 1 3 21
%e A256095 7: 28 1 1 2 2 1 7 28
%e A256095 8: 36 1 3 6 2 3 3 4 36
%e A256095 9: 45 1 3 3 5 15 3 1 9 45
%e A256095 10: 55 1 1 1 5 5 1 1 1 5 55
%e A256095 11: 66 1 3 6 2 3 3 2 6 3 11 66
%e A256095 12: 78 1 3 6 2 3 3 2 6 3 1 6 78
%e A256095 13: 91 1 1 1 1 1 7 7 1 1 1 1 13 91
%e A256095 14: 105 1 3 3 5 15 21 7 3 15 5 3 3 7 105
%e A256095 ...
%p A256095 T:= (i,j) -> igcd(i*(i+1)/2,j*(j+1)/2):
%p A256095 seq(seq(T(i,j),j=0..i),i=0..20); # _Robert Israel_, Jan 20 2020
%o A256095 (PARI) tabl(nn) = {for (n=0, nn, trn = n*(n+1)/2; for (k=0, n, print1(gcd(trn, k*(k+1)/2), ", ");); print(););} \\ _Michel Marcus_, Mar 17 2015
%Y A256095 Cf. A000217, A144437.
%Y A256095 T(2n,n) gives A026741.
%K A256095 nonn,easy,tabl
%O A256095 0,4
%A A256095 _Wolfdieter Lang_, Mar 17 2015