λ
Harmonic Matrix

349,721

191 × 1831
Deficient Odd Composite

349,721 has digital root 8. The neighboring primes are 349717 and 349729; its proper-divisor sum differs from the starting integer by -347,698.

Prime Factor Structure

Factorization String 191 × 1831
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 351,744
Proper Divisor Sum 2,023
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #349717 ← → #349729

Radix Representation

Decimal 349721
Binary 1010101011000011001 (19 bits)
Octal 0o1253031
Hexadecimal 0x55619

Divisor Catalog (4)

1 191 1,831 349,721

Collatz Trajectory (228 steps to reach 1)

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

349,721 1,049,164 524,582 262,291 786,874 393,437 1,180,312 590,156 295,078 147,539 442,618 221,309 663,928 331,964 165,982 82,991 248,974 124,487 373,462 186,731 560,194 280,097 840,292 420,146 210,073 630,220 315,110 157,555 472,666 236,333 709,000 354,500 177,250 88,625 265,876 132,938 66,469 199,408 99,704 49,852 24,926 12,463 37,390 18,695 56,086 28,043 84,130 42,065 126,196 63,098 31,549 94,648 47,324 23,662 11,831 35,494 17,747 53,242 26,621 79,864

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