31,801

7² × 11 × 59

31,801 has digital root 4. The neighboring primes are 31799 and 31817; its proper-divisor sum differs from the starting integer by -22,562.

Prime Factor Structure

Factorization String 7^2 × 11 × 59

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 41,040

Proper Divisor Sum 9,239

Digit Sum / Digital Root 13 (Root: 4)

Adjacent Primes #31799 ← → #31817

Radix Representation

Decimal	31801
Binary	111110000111001 (15 bits)
Octal	0o76071
Hexadecimal	0x7C39

Divisor Catalog (12)

1 7 11 49 59 77 413 539 649 2,891 4,543 31,801

Collatz Trajectory (129 steps to reach 1)

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

31,801 95,404 47,702 23,851 71,554 35,777 107,332 53,666 26,833 80,500 40,250 20,125 60,376 30,188 15,094 7,547 22,642 11,321 33,964 16,982 8,491 25,474 12,737 38,212 19,106 9,553 28,660 14,330 7,165 21,496 10,748 5,374 2,687 8,062 4,031 12,094 6,047 18,142 9,071 27,214 13,607 40,822 20,411 61,234 30,617 91,852 45,926 22,963 68,890 34,445 103,336 51,668 25,834 12,917 38,752 19,376 9,688 4,844 2,422 1,211

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