λ
Harmonic Matrix

6,048,654

2 × 3 × 431 × 2339
Abundant Even Composite

6,048,654 has digital root 6. The neighboring primes are 6048641 and 6048659; its proper-divisor sum differs from the starting integer by 33,252.

Prime Factor Structure

Factorization String 2 × 3 × 431 × 2339
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 12,130,560
Proper Divisor Sum 6,081,906
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #6048641 ← → #6048659

Radix Representation

Decimal 6048654
Binary 10111000100101110001110 (23 bits)
Octal 0o27045616
Hexadecimal 0x5C4B8E

Divisor Catalog (16)

1 2 3 6 431 862 1,293 2,339 2,586 4,678 7,017 14,034 1,008,109 2,016,218 3,024,327 6,048,654

Collatz Trajectory (196 steps to reach 1)

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

6,048,654 3,024,327 9,072,982 4,536,491 13,609,474 6,804,737 20,414,212 10,207,106 5,103,553 15,310,660 7,655,330 3,827,665 11,482,996 5,741,498 2,870,749 8,612,248 4,306,124 2,153,062 1,076,531 3,229,594 1,614,797 4,844,392 2,422,196 1,211,098 605,549 1,816,648 908,324 454,162 227,081 681,244 340,622 170,311 510,934 255,467 766,402 383,201 1,149,604 574,802 287,401 862,204 431,102 215,551 646,654 323,327 969,982 484,991 1,454,974 727,487 2,182,462 1,091,231 3,273,694 1,636,847 4,910,542 2,455,271 7,365,814 3,682,907 11,048,722 5,524,361 16,573,084 8,286,542

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