λ
Harmonic Matrix

752,259

3 × 250753
Deficient Odd Composite

752,259 has digital root 3. The neighboring primes are 752251 and 752263; its proper-divisor sum differs from the starting integer by -501,502.

Prime Factor Structure

Factorization String 3 × 250753
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 1,003,016
Proper Divisor Sum 250,757
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #752251 ← → #752263

Radix Representation

Decimal 752259
Binary 10110111101010000011 (20 bits)
Octal 0o2675203
Hexadecimal 0xB7A83

Divisor Catalog (4)

1 3 250,753 752,259

Collatz Trajectory (61 steps to reach 1)

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

752,259 2,256,778 1,128,389 3,385,168 1,692,584 846,292 423,146 211,573 634,720 317,360 158,680 79,340 39,670 19,835 59,506 29,753 89,260 44,630 22,315 66,946 33,473 100,420 50,210 25,105 75,316 37,658 18,829 56,488 28,244 14,122 7,061 21,184 10,592 5,296 2,648 1,324 662 331 994 497 1,492 746 373 1,120 560 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4

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