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A225399
Number of nontrivial triangular numbers dividing triangular(n).
2
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).
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
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, May 06 2013
STATUS
approved