λ
Harmonic Matrix

728,930

2 × 5 × 72893
Deficient Even Composite

728,930 has digital root 2. The neighboring primes are 728929 and 728941; its proper-divisor sum differs from the starting integer by -145,768.

Prime Factor Structure

Factorization String 2 × 5 × 72893
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 1,312,092
Proper Divisor Sum 583,162
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #728929 ← → #728941

Radix Representation

Decimal 728930
Binary 10110001111101100010 (20 bits)
Octal 0o2617542
Hexadecimal 0xB1F62

Divisor Catalog (8)

1 2 5 10 72,893 145,786 364,465 728,930

Collatz Trajectory (74 steps to reach 1)

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

728,930 364,465 1,093,396 546,698 273,349 820,048 410,024 205,012 102,506 51,253 153,760 76,880 38,440 19,220 9,610 4,805 14,416 7,208 3,604 1,802 901 2,704 1,352 676 338 169 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22

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