λ
Harmonic Matrix

8,387,405

5 × 13 × 129037
Deficient Odd Composite

8,387,405 has digital root 8. The neighboring primes are 8387377 and 8387413; its proper-divisor sum differs from the starting integer by -5,935,618.

Prime Factor Structure

Factorization String 5 × 13 × 129037
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 10,839,192
Proper Divisor Sum 2,451,787
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #8387377 ← → #8387413

Radix Representation

Decimal 8387405
Binary 11111111111101101001101 (23 bits)
Octal 0o37775515
Hexadecimal 0x7FFB4D

Divisor Catalog (8)

1 5 13 65 129,037 645,185 1,677,481 8,387,405

Collatz Trajectory (199 steps to reach 1)

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

8,387,405 25,162,216 12,581,108 6,290,554 3,145,277 9,435,832 4,717,916 2,358,958 1,179,479 3,538,438 1,769,219 5,307,658 2,653,829 7,961,488 3,980,744 1,990,372 995,186 497,593 1,492,780 746,390 373,195 1,119,586 559,793 1,679,380 839,690 419,845 1,259,536 629,768 314,884 157,442 78,721 236,164 118,082 59,041 177,124 88,562 44,281 132,844 66,422 33,211 99,634 49,817 149,452 74,726 37,363 112,090 56,045 168,136 84,068 42,034 21,017 63,052 31,526 15,763 47,290 23,645 70,936 35,468 17,734 8,867

More profiles

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