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

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

Offset: 0

Author

Alex Ratushnyak, May 06 2013

Keywords

• nonn

Comments

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

Examples

			triangular(3) = 6 is divisible by triangular(2) = 3, so a(3) = 1.
triangular(8) = 36 is divisible by triangular(2) = 3 and triangular(3) = 6, so a(8) = 2.
		

Crossrefs

Cf. A000217, A225400.

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

Programs

C

#include 
int main() {
  unsigned long long c, i, j, t, tn;
  for (i = tn = 0; i < (1ULL<<32); i++) {
        for (c=0, tn += i, t = j = 3; t*2 <= tn; t+=j, ++j)
                if (tn % t == 0)  ++c;
        printf("%llu, ", c);
  }
  return 0;
}

Maple

A225399 := proc(n)
    option remember ;
    local a,tn,i;
    a := 0 ;
    tn := A000217(n) ;
    for i from 2 to n-1 do
        if modp(tn,A000217(i))=0 then
            a := a+1 ;
        end if;
    end do:
    a;
end proc:
seq(A225399(n),n=0..80) ; # R. J. Mathar, Jan 12 2024

Mathematica

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 *)

Formula

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