λ
Harmonic Matrix

313,770

2 × 3 × 5 × 10459
Abundant Even Composite

313,770 has digital root 3. The neighboring primes are 313763 and 313777; its proper-divisor sum differs from the starting integer by 125,580.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 10459
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 753,120
Proper Divisor Sum 439,350
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #313763 ← → #313777

Radix Representation

Decimal 313770
Binary 1001100100110101010 (19 bits)
Octal 0o1144652
Hexadecimal 0x4C9AA

Divisor Catalog (16)

1 2 3 5 6 10 15 30 10,459 20,918 31,377 52,295 62,754 104,590 156,885 313,770

Collatz Trajectory (140 steps to reach 1)

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

313,770 156,885 470,656 235,328 117,664 58,832 29,416 14,708 7,354 3,677 11,032 5,516 2,758 1,379 4,138 2,069 6,208 3,104 1,552 776 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350

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