λ
Harmonic Matrix

2,049,743

509 × 4027
Deficient Odd Composite

2,049,743 has digital root 2. The neighboring primes are 2049727 and 2049787; its proper-divisor sum differs from the starting integer by -2,045,206.

Prime Factor Structure

Factorization String 509 × 4027
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 2,054,280
Proper Divisor Sum 4,537
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #2049727 ← → #2049787

Radix Representation

Decimal 2049743
Binary 111110100011011001111 (21 bits)
Octal 0o7643317
Hexadecimal 0x1F46CF

Divisor Catalog (4)

1 509 4,027 2,049,743

Collatz Trajectory (215 steps to reach 1)

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

2,049,743 6,149,230 3,074,615 9,223,846 4,611,923 13,835,770 6,917,885 20,753,656 10,376,828 5,188,414 2,594,207 7,782,622 3,891,311 11,673,934 5,836,967 17,510,902 8,755,451 26,266,354 13,133,177 39,399,532 19,699,766 9,849,883 29,549,650 14,774,825 44,324,476 22,162,238 11,081,119 33,243,358 16,621,679 49,865,038 24,932,519 74,797,558 37,398,779 112,196,338 56,098,169 168,294,508 84,147,254 42,073,627 126,220,882 63,110,441 189,331,324 94,665,662 47,332,831 141,998,494 70,999,247 212,997,742 106,498,871 319,496,614 159,748,307 479,244,922 239,622,461 718,867,384 359,433,692 179,716,846 89,858,423 269,575,270 134,787,635 404,362,906 202,181,453 606,544,360

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