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A225399
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Number of nontrivial triangular numbers dividing triangular(n).
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2
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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
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OFFSET
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0,9
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COMMENTS
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Number of triangular numbers t such that t divides triangular(n), and 1 < t < triangular(n).
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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option remember ;
local a, tn, i;
a := 0 ;
for i from 2 to n-1 do
a := a+1 ;
end if;
end do:
a;
end proc:
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MATHEMATICA
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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 *)
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PROG
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(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;
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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