λ
Harmonic Matrix

8,188,797

3 × 193 × 14143
Deficient Odd Composite

8,188,797 has digital root 3. The neighboring primes are 8188793 and 8188799; its proper-divisor sum differs from the starting integer by -5,401,850.

Prime Factor Structure

Factorization String 3 × 193 × 14143
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 10,975,744
Proper Divisor Sum 2,786,947
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #8188793 ← → #8188799

Radix Representation

Decimal 8188797
Binary 11111001111001101111101 (23 bits)
Octal 0o37171575
Hexadecimal 0x7CF37D

Divisor Catalog (8)

1 3 193 579 14,143 42,429 2,729,599 8,188,797

Collatz Trajectory (199 steps to reach 1)

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

8,188,797 24,566,392 12,283,196 6,141,598 3,070,799 9,212,398 4,606,199 13,818,598 6,909,299 20,727,898 10,363,949 31,091,848 15,545,924 7,772,962 3,886,481 11,659,444 5,829,722 2,914,861 8,744,584 4,372,292 2,186,146 1,093,073 3,279,220 1,639,610 819,805 2,459,416 1,229,708 614,854 307,427 922,282 461,141 1,383,424 691,712 345,856 172,928 86,464 43,232 21,616 10,808 5,404 2,702 1,351 4,054 2,027 6,082 3,041 9,124 4,562 2,281 6,844 3,422 1,711 5,134 2,567 7,702 3,851 11,554 5,777 17,332 8,666

More profiles

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