128,013

3 × 71 × 601

128,013 factors as 3 × 71 × 601. Its 8 positive divisors give a proper-divisor sum of 45,363, so this integer is deficient. The Collatz stopping time is 149 steps.

Prime Factor Structure

Factorization String 3 × 71 × 601

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 173,376

Proper Divisor Sum 45,363

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #127997 ← → #128021

Radix Representation

Decimal	128013
Binary	11111010000001101 (17 bits)
Octal	0o372015
Hexadecimal	0x1F40D

Divisor Catalog (8)

1 3 71 213 601 1,803 42,671 128,013

Collatz Trajectory (149 steps to reach 1)

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

128,013 384,040 192,020 96,010 48,005 144,016 72,008 36,004 18,002 9,001 27,004 13,502 6,751 20,254 10,127 30,382 15,191 45,574 22,787 68,362 34,181 102,544 51,272 25,636 12,818 6,409 19,228 9,614 4,807 14,422 7,211 21,634 10,817 32,452 16,226 8,113 24,340 12,170 6,085 18,256 9,128 4,564 2,282 1,141 3,424 1,712 856 428 214 107 322 161 484 242 121 364 182 91 274 137

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