λ
Harmonic Matrix

1,678,082

2 × 7 × 67 × 1789
Deficient Even Composite

1,678,082 has digital root 5. The neighboring primes are 1678073 and 1678091; its proper-divisor sum differs from the starting integer by -434,884.

Prime Factor Structure

Factorization String 2 × 7 × 67 × 1789
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 2,921,280
Proper Divisor Sum 1,243,198
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #1678073 ← → #1678091

Radix Representation

Decimal 1678082
Binary 110011001101100000010 (21 bits)
Octal 0o6315402
Hexadecimal 0x199B02

Divisor Catalog (16)

1 2 7 14 67 134 469 938 1,789 3,578 12,523 25,046 119,863 239,726 839,041 1,678,082

Collatz Trajectory (57 steps to reach 1)

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

1,678,082 839,041 2,517,124 1,258,562 629,281 1,887,844 943,922 471,961 1,415,884 707,942 353,971 1,061,914 530,957 1,592,872 796,436 398,218 199,109 597,328 298,664 149,332 74,666 37,333 112,000 56,000 28,000 14,000 7,000 3,500 1,750 875 2,626 1,313 3,940 1,970 985 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16 8 4 2 1

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