337,953

3 × 7² × 11² × 19

337,953 factors as 3 × 7^2 × 11^2 × 19. Its 36 positive divisors give a proper-divisor sum of 268,527, so this integer is deficient. The Collatz stopping time is 109 steps.

Prime Factor Structure

Factorization String 3 × 7^2 × 11^2 × 19

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 606,480

Proper Divisor Sum 268,527

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #337949 ← → #337957

Radix Representation

Decimal	337953
Binary	1010010100000100001 (19 bits)
Octal	0o1224041
Hexadecimal	0x52821

Divisor Catalog (36)

1 3 7 11 19 21 33 49 57 77 121 133 147 209 231 363 399 539 627 847 931 1,463 1,617 2,299 2,541 2,793 4,389 5,929 6,897 10,241 16,093 17,787 30,723 48,279 112,651 337,953

Collatz Trajectory (109 steps to reach 1)

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

337,953 1,013,860 506,930 253,465 760,396 380,198 190,099 570,298 285,149 855,448 427,724 213,862 106,931 320,794 160,397 481,192 240,596 120,298 60,149 180,448 90,224 45,112 22,556 11,278 5,639 16,918 8,459 25,378 12,689 38,068 19,034 9,517 28,552 14,276 7,138 3,569 10,708 5,354 2,677 8,032 4,016 2,008 1,004 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158

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