525,664

2⁵ × 16427

525,664 has digital root 1. The neighboring primes are 525649 and 525671; its proper-divisor sum differs from the starting integer by -16,364.

Prime Factor Structure

Factorization String 2^5 × 16427

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,034,964

Proper Divisor Sum 509,300

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #525649 ← → #525671

Radix Representation

Decimal	525664
Binary	10000000010101100000 (20 bits)
Octal	0o2002540
Hexadecimal	0x80560

Divisor Catalog (12)

1 2 4 8 16 32 16,427 32,854 65,708 131,416 262,832 525,664

Collatz Trajectory (164 steps to reach 1)

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

525,664 262,832 131,416 65,708 32,854 16,427 49,282 24,641 73,924 36,962 18,481 55,444 27,722 13,861 41,584 20,792 10,396 5,198 2,599 7,798 3,899 11,698 5,849 17,548 8,774 4,387 13,162 6,581 19,744 9,872 4,936 2,468 1,234 617 1,852 926 463 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762 881 2,644 1,322 661 1,984 992 496 248 124 62 31 94

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