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

0,9

Comments

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

Links

Table of n, a(n) for n=0..86.

Formula

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

Example

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.

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 *)

Prog

(C)
#include <stdio.h>
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;
}

Crossrefs

Cf. A000217, A225400.

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

Sequence in context: A257076 A109265 A184334 * A035668 A307757 A215283

Adjacent sequences: A225396 A225397 A225398 * A225400 A225401 A225402

Keyword

nonn

Author

Alex Ratushnyak, May 06 2013

Status

approved