λ
Harmonic Matrix

3,143,664

24 × 33 × 19 × 383
Abundant Even Composite

3,143,664 has digital root 9. The neighboring primes are 3143641 and 3143671; its proper-divisor sum differs from the starting integer by 3,235,872.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 19 × 383
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 9,523,200
Proper Divisor Sum 6,379,536
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #3143641 ← → #3143671

Radix Representation

Decimal 3143664
Binary 1011111111011111110000 (22 bits)
Octal 0o13773760
Hexadecimal 0x2FF7F0

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 16 18 19 24 27 36 38 48 54 57 72 76 108 114 144 152 171 216 228 304 342 383 432 456 513 684 766 912 1,026 1,149 1,368 1,532 2,052 2,298 2,736 3,064 3,447 4,104 4,596 6,128 6,894 7,277 8,208 9,192 10,341 13,788 14,554 18,384 20,682 21,831 27,576 29,108

Collatz Trajectory (164 steps to reach 1)

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

3,143,664 1,571,832 785,916 392,958 196,479 589,438 294,719 884,158 442,079 1,326,238 663,119 1,989,358 994,679 2,984,038 1,492,019 4,476,058 2,238,029 6,714,088 3,357,044 1,678,522 839,261 2,517,784 1,258,892 629,446 314,723 944,170 472,085 1,416,256 708,128 354,064 177,032 88,516 44,258 22,129 66,388 33,194 16,597 49,792 24,896 12,448 6,224 3,112 1,556 778 389 1,168 584 292 146 73 220 110 55 166 83 250 125 376 188 94

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