Factorial–triangular ratio

Factorial–triangular ratio is the mathematical operation in which we take a number, find factorial by multiplying every number from one to that number, find triangular by adding every number from one to that number, then divide the resulting numbers. For example, take 5. The factorial of 5 is 120, since 1×2×3×4×5, and the triangular is 15 since 1+2+3+4+5. Then we divide 120 by 15, and we get the final answer, 8.

Here's the ratios of the first ten numbers:


 * 1 = (1) / (1) = 1
 * 2 = (1×2) / (1+2) = 2 / 3 = 0.
 * 3 = (1×2×3) / (1+2+3) = 6 / 6 = 1
 * 4 = (1×2×3×4) / (1+2+3+4) = 24 / 10 = 2.4
 * 5 = (1×2×3×4×5) / (1+2+3+4+5) = 120 / 15 = 8
 * 6 = (1×2×3×4×5×6) / (1+2+3+4+5+6) = 720 / 21 = 34.
 * 7 = (1×2×3×4×5×6×7) / (1+2+3+4+5+6+7) = 5040 / 28 = 180
 * 8 = (1×2×3×4×5×6×7×8) / (1+2+3+4+5+6+7+8) = 40320 / 36 = 1120
 * 9 = (1×2×3×4×5×6×7×8×9) / (1+2+3+4+5+6+7+8+9) = 362880 / 45 = 8064
 * 10 = (1×2×3×4×5×6×7×8×9×10) / (1+2+3+4+5+6+7+8+9+10) = 3628800 / 55 = 65978.

Notice there are two numbers (1 and 3) in which the factorial-triangular ratio are 1, while 2 is the only number in which the ratio is less than 1.