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693,105

3 × 5 × 72 × 23 × 41
Deficient Odd Composite

693,105 factors as 3 × 5 × 7^2 × 23 × 41. Its 48 positive divisors give a proper-divisor sum of 685,839, so this integer is deficient. The Collatz stopping time is 74 steps.

Prime Factor Structure

Factorization String 3 × 5 × 7^2 × 23 × 41
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,378,944
Proper Divisor Sum 685,839
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #693103 ← → #693127

Radix Representation

Decimal 693105
Binary 10101001001101110001 (20 bits)
Octal 0o2511561
Hexadecimal 0xA9371

Divisor Catalog (48)

1 3 5 7 15 21 23 35 41 49 69 105 115 123 147 161 205 245 287 345 483 615 735 805 861 943 1,127 1,435 2,009 2,415 2,829 3,381 4,305 4,715 5,635 6,027 6,601 10,045 14,145 16,905 19,803 30,135 33,005 46,207 99,015 138,621 231,035 693,105

Collatz Trajectory (74 steps to reach 1)

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

693,105 2,079,316 1,039,658 519,829 1,559,488 779,744 389,872 194,936 97,468 48,734 24,367 73,102 36,551 109,654 54,827 164,482 82,241 246,724 123,362 61,681 185,044 92,522 46,261 138,784 69,392 34,696 17,348 8,674 4,337 13,012 6,506 3,253 9,760 4,880 2,440 1,220 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22

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