A225399 - OEIS

%I #16 Jan 12 2024 09:02:58

%S 0,0,0,1,0,1,1,0,2,2,0,2,2,0,3,4,0,1,1,1,6,2,0,2,4,0,1,3,0,2,2,0,3,1,

%T 0,8,2,0,1,5,1,2,2,0,7,3,0,2,4,0,2,3,0,1,4,3,4,1,0,4,4,0,2,5,1,3,1,0,

%U 2,4,0,3,3,0,2,5,0,4,1,1,7,1,0,3,8,0,1

%N Number of nontrivial triangular numbers dividing triangular(n).

%C Number of triangular numbers t such that t divides triangular(n), and 1 < t < triangular(n).

%F a(n) = A076982(n) - 2 for n > 1.

%e triangular(3) = 6 is divisible by triangular(2) = 3, so a(3) = 1.

%e triangular(8) = 36 is divisible by triangular(2) = 3 and triangular(3) = 6, so a(8) = 2.

%p A225399 := proc(n)

%p     option remember ;

%p     local a,tn,i;

%p     a := 0 ;

%p     tn := A000217(n) ;

%p     for i from 2 to n-1 do

%p         if modp(tn,A000217(i))=0 then

%p             a := a+1 ;

%p         end if;

%p     end do:

%p     a;

%p end proc:

%p seq(A225399(n),n=0..80) ; # _R. J. Mathar_, Jan 12 2024

%t tri = Table[n (n + 1)/2, {n, 100}]; Table[cnt = 0; Do[If[Mod[tri[[n]], tri[[k]]] == 0, cnt++], {k, 2, n - 1}]; cnt, {n, 0, Length[tri]}] (* _T. D. Noe_, May 07 2013 *)

%o (C)

%o #include <stdio.h>

%o int main() {

%o   unsigned long long c, i, j, t, tn;

%o   for (i = tn = 0; i < (1ULL<<32); i++) {

%o         for (c=0, tn += i, t = j = 3; t*2 <= tn; t+=j, ++j)

%o                 if (tn % t == 0)  ++c;

%o         printf("%llu, ", c);

%o   }

%o   return 0;

%o }

%Y Cf. A000217, A225400.

%Y Cf. A076982, A076983, A084260, A137281, A141283.

%K nonn

%O 0,9

%A _Alex Ratushnyak_, May 06 2013