λ
Harmonic Matrix

8,382,399

3 × 1361 × 2053
Deficient Odd Composite

8,382,399 has digital root 6. The neighboring primes are 8382389 and 8382433; its proper-divisor sum differs from the starting integer by -5,574,606.

Prime Factor Structure

Factorization String 3 × 1361 × 2053
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 11,190,192
Proper Divisor Sum 2,807,793
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #8382389 ← → #8382433

Radix Representation

Decimal 8382399
Binary 11111111110011110111111 (23 bits)
Octal 0o37763677
Hexadecimal 0x7FE7BF

Divisor Catalog (8)

1 3 1,361 2,053 4,083 6,159 2,794,133 8,382,399

Collatz Trajectory (137 steps to reach 1)

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

8,382,399 25,147,198 12,573,599 37,720,798 18,860,399 56,581,198 28,290,599 84,871,798 42,435,899 127,307,698 63,653,849 190,961,548 95,480,774 47,740,387 143,221,162 71,610,581 214,831,744 107,415,872 53,707,936 26,853,968 13,426,984 6,713,492 3,356,746 1,678,373 5,035,120 2,517,560 1,258,780 629,390 314,695 944,086 472,043 1,416,130 708,065 2,124,196 1,062,098 531,049 1,593,148 796,574 398,287 1,194,862 597,431 1,792,294 896,147 2,688,442 1,344,221 4,032,664 2,016,332 1,008,166 504,083 1,512,250 756,125 2,268,376 1,134,188 567,094 283,547 850,642 425,321 1,275,964 637,982 318,991

More profiles

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