665,353

13² × 31 × 127

665,353 factors as 13^2 × 31 × 127. Its 12 positive divisors give a proper-divisor sum of 84,215, so this integer is deficient. The Collatz stopping time is 92 steps.

Prime Factor Structure

Factorization String 13^2 × 31 × 127

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 749,568

Proper Divisor Sum 84,215

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #665351 ← → #665359

Radix Representation

Decimal	665353
Binary	10100010011100001001 (20 bits)
Octal	0o2423411
Hexadecimal	0xA2709

Divisor Catalog (12)

1 13 31 127 169 403 1,651 3,937 5,239 21,463 51,181 665,353

Collatz Trajectory (92 steps to reach 1)

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

665,353 1,996,060 998,030 499,015 1,497,046 748,523 2,245,570 1,122,785 3,368,356 1,684,178 842,089 2,526,268 1,263,134 631,567 1,894,702 947,351 2,842,054 1,421,027 4,263,082 2,131,541 6,394,624 3,197,312 1,598,656 799,328 399,664 199,832 99,916 49,958 24,979 74,938 37,469 112,408 56,204 28,102 14,051 42,154 21,077 63,232 31,616 15,808 7,904 3,952 1,976 988 494 247 742 371 1,114 557 1,672 836 418 209 628 314 157 472 236 118

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