520,125

3 × 5³ × 19 × 73

520,125 factors as 3 × 5^3 × 19 × 73. Its 32 positive divisors give a proper-divisor sum of 403,395, so this integer is deficient. The Collatz stopping time is 89 steps.

Prime Factor Structure

Factorization String 3 × 5^3 × 19 × 73

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 923,520

Proper Divisor Sum 403,395

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #520123 ← → #520129

Radix Representation

Decimal	520125
Binary	1111110111110111101 (19 bits)
Octal	0o1767675
Hexadecimal	0x7EFBD

Divisor Catalog (32)

1 3 5 15 19 25 57 73 75 95 125 219 285 365 375 475 1,095 1,387 1,425 1,825 2,375 4,161 5,475 6,935 7,125 9,125 20,805 27,375 34,675 104,025 173,375 520,125

Collatz Trajectory (89 steps to reach 1)

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

520,125 1,560,376 780,188 390,094 195,047 585,142 292,571 877,714 438,857 1,316,572 658,286 329,143 987,430 493,715 1,481,146 740,573 2,221,720 1,110,860 555,430 277,715 833,146 416,573 1,249,720 624,860 312,430 156,215 468,646 234,323 702,970 351,485 1,054,456 527,228 263,614 131,807 395,422 197,711 593,134 296,567 889,702 444,851 1,334,554 667,277 2,001,832 1,000,916 500,458 250,229 750,688 375,344 187,672 93,836 46,918 23,459 70,378 35,189 105,568 52,784 26,392 13,196 6,598 3,299

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