cp's OEIS Frontend

A225399 Number of nontrivial triangular numbers dividing triangular(n).

%I A225399 #16 Jan 12 2024 09:02:58
%S A225399 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 A225399 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 A225399 2,4,0,3,3,0,2,5,0,4,1,1,7,1,0,3,8,0,1
%N A225399 Number of nontrivial triangular numbers dividing triangular(n).
%C A225399 Number of triangular numbers t such that t divides triangular(n), and 1 < t < triangular(n).
%F A225399 a(n) = A076982(n) - 2 for n > 1.
%e A225399 triangular(3) = 6 is divisible by triangular(2) = 3, so a(3) = 1.
%e A225399 triangular(8) = 36 is divisible by triangular(2) = 3 and triangular(3) = 6, so a(8) = 2.
%p A225399 A225399 := proc(n)
%p A225399     option remember ;
%p A225399     local a,tn,i;
%p A225399     a := 0 ;
%p A225399     tn := A000217(n) ;
%p A225399     for i from 2 to n-1 do
%p A225399         if modp(tn,A000217(i))=0 then
%p A225399             a := a+1 ;
%p A225399         end if;
%p A225399     end do:
%p A225399     a;
%p A225399 end proc:
%p A225399 seq(A225399(n),n=0..80) ; # _R. J. Mathar_, Jan 12 2024
%t A225399 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 A225399 (C)
%o A225399 #include <stdio.h>
%o A225399 int main() {
%o A225399   unsigned long long c, i, j, t, tn;
%o A225399   for (i = tn = 0; i < (1ULL<<32); i++) {
%o A225399         for (c=0, tn += i, t = j = 3; t*2 <= tn; t+=j, ++j)
%o A225399                 if (tn % t == 0)  ++c;
%o A225399         printf("%llu, ", c);
%o A225399   }
%o A225399   return 0;
%o A225399 }
%Y A225399 Cf. A000217, A225400.
%Y A225399 Cf. A076982, A076983, A084260, A137281, A141283.
%K A225399 nonn
%O A225399 0,9
%A A225399 _Alex Ratushnyak_, May 06 2013