82,917

3³ × 37 × 83

82,917 is odd and not a perfect square. Its factorization is 3^3 × 37 × 83 and its 16 divisors sum to 127,680.

Prime Factor Structure

Factorization String 3^3 × 37 × 83

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 127,680

Proper Divisor Sum 44,763

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #82913 ← → #82939

Radix Representation

Decimal	82917
Binary	10100001111100101 (17 bits)
Octal	0o241745
Hexadecimal	0x143E5

Divisor Catalog (16)

1 3 9 27 37 83 111 249 333 747 999 2,241 3,071 9,213 27,639 82,917

Collatz Trajectory (63 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

82,917 248,752 124,376 62,188 31,094 15,547 46,642 23,321 69,964 34,982 17,491 52,474 26,237 78,712 39,356 19,678 9,839 29,518 14,759 44,278 22,139 66,418 33,209 99,628 49,814 24,907 74,722 37,361 112,084 56,042 28,021 84,064 42,032 21,016 10,508 5,254 2,627 7,882 3,941 11,824 5,912 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16

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