%I #13 Sep 16 2021 13:31:19

%S 2,4,10,6,7,10,9,10,13,12,13,22,15,16,22,18,19,22,21,22,25,24,25,37,

%T 27,28,37,30,31,37,33,34,37,36,37,46,39,40,46,42,43,46,45,46,52,48,49,

%U 58,51,52,58,54,55,58,57,58,61,60,61,73,63,64,73,66,67,70,69,70,73,72,73

%N Smallest m>n such that the m-th and n-th triangular numbers are coprime.

%H Reinhard Zumkeller, <a href="/A130334/b130334.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>

%F a(n) > n+1 for n>1; a(n) > n+2 for n with n mod 3 = 0;

%F a(n) = n + A130335(n).

%o (Python)

%o from math import gcd

%o def A130334(n):

%o k, Tn, Tm = n+1, n*(n+1)//2, (n+1)*(n+2)//2

%o while gcd(Tn,Tm) != 1:

%o k += 1

%o Tm += k

%o return k # _Chai Wah Wu_, Sep 16 2021

%Y Cf. A000217, A026741, A109007, A130335.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 28 2007