A126247 - OEIS

%I #20 Feb 01 2019 03:02:33

%S 1,1,1,2,1,2,3,1,2,6,1,2,9,1,2,8,5,6,5,1,4,18,3,3,13,7,4,10,5,6,15,3,

%T 8,12,2,6,33,9,3,12,9,10,17,3,8,42,7,6,21,9,6,22,17,9,9,5,16,54,5,6,

%U 57,13,8,17,9,18,29,8,9,30,11,12,69,13,7,17,12,22,23,8,26,78,9,8,43,25,12,36

%N a(n) is the number of triangular numbers, from among (T(1), T(2), T(3), ..., T(n)), which are coprime to T(n), where T(n) = n(n+1)/2 is the n-th triangular number.

%e T(10) = 10*11/2 = 55. The six triangular numbers which are coprime to 55 and are <= 55 are T(1)=1, T(2)=3, T(3)=6, T(6)=21, T(7)=28 and T(8)=36. So a(10) = 6.

%p a:=proc(n) local ct,i: ct:=0: for i from 1 to n do if gcd(i*(i+1)/2,n*(n+1)/2)=1 then ct:=ct+1 else ct:=ct fi: od: ct: end: seq(a(n),n=1..100); # _Emeric Deutsch_, Mar 24 2007

%o (PARI) a(n) = sum(k=1, n, gcd(n*(n+1)/2, k*(k+1)/2) == 1); \\ _Michel Marcus_, Feb 01 2019

%Y Cf. A000217.

%K nonn

%O 1,4

%A _Leroy Quet_, Mar 08 2007

%E More terms from _Emeric Deutsch_, Mar 24 2007