329,967

3³ × 11² × 101

329,967 factors as 3^3 × 11^2 × 101. Its 24 positive divisors give a proper-divisor sum of 212,673, so this integer is deficient. The Collatz stopping time is 197 steps.

Prime Factor Structure

Factorization String 3^3 × 11^2 × 101

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 542,640

Proper Divisor Sum 212,673

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #329957 ← → #329969

Radix Representation

Decimal	329967
Binary	1010000100011101111 (19 bits)
Octal	0o1204357
Hexadecimal	0x508EF

Divisor Catalog (24)

1 3 9 11 27 33 99 101 121 297 303 363 909 1,089 1,111 2,727 3,267 3,333 9,999 12,221 29,997 36,663 109,989 329,967

Collatz Trajectory (197 steps to reach 1)

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

329,967 989,902 494,951 1,484,854 742,427 2,227,282 1,113,641 3,340,924 1,670,462 835,231 2,505,694 1,252,847 3,758,542 1,879,271 5,637,814 2,818,907 8,456,722 4,228,361 12,685,084 6,342,542 3,171,271 9,513,814 4,756,907 14,270,722 7,135,361 21,406,084 10,703,042 5,351,521 16,054,564 8,027,282 4,013,641 12,040,924 6,020,462 3,010,231 9,030,694 4,515,347 13,546,042 6,773,021 20,319,064 10,159,532 5,079,766 2,539,883 7,619,650 3,809,825 11,429,476 5,714,738 2,857,369 8,572,108 4,286,054 2,143,027 6,429,082 3,214,541 9,643,624 4,821,812 2,410,906 1,205,453 3,616,360 1,808,180 904,090 452,045

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