Today’s Puzzle:

A formula for the nth triangular number is n(n+1)/2. Centered triangular numbers are the sum of three consecutive triangular numbers. What would be a formula for finding centered triangular numbers? What value of n in your formula would produce the number 1786?

Factors of 1786:

• 1786 is a composite number.
• Prime factorization: 1786 = 2 × 19 × 47.
• 1786 has no exponents greater than 1 in its prime factorization, so √1786 cannot be simplified.
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1786 has exactly 8 factors.
• The factors of 1786 are outlined with their factor pair partners in the graphic below.

More About the Number 1786:

From OEIS.org we learn that 1786³ = 5,696,975,656. Notice that all those digits are 5 or greater.

1786 is 1G1 in base35,
because 1(35²) + 16(35) + 1(1) = 1786.