λ
Harmonic Matrix

8,124,389

7 × 13 × 73 × 1223
Deficient Odd Composite

8,124,389 has digital root 8. The neighboring primes are 8124367 and 8124397; its proper-divisor sum differs from the starting integer by -6,104,266.

Prime Factor Structure

Factorization String 7 × 13 × 73 × 1223
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 10,144,512
Proper Divisor Sum 2,020,123
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #8124367 ← → #8124397

Radix Representation

Decimal 8124389
Binary 11110111111011111100101 (23 bits)
Octal 0o36773745
Hexadecimal 0x7BF7E5

Divisor Catalog (16)

1 7 13 73 91 511 949 1,223 6,643 8,561 15,899 89,279 111,293 624,953 1,160,627 8,124,389

Collatz Trajectory (85 steps to reach 1)

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

8,124,389 24,373,168 12,186,584 6,093,292 3,046,646 1,523,323 4,569,970 2,284,985 6,854,956 3,427,478 1,713,739 5,141,218 2,570,609 7,711,828 3,855,914 1,927,957 5,783,872 2,891,936 1,445,968 722,984 361,492 180,746 90,373 271,120 135,560 67,780 33,890 16,945 50,836 25,418 12,709 38,128 19,064 9,532 4,766 2,383 7,150 3,575 10,726 5,363 16,090 8,045 24,136 12,068 6,034 3,017 9,052 4,526 2,263 6,790 3,395 10,186 5,093 15,280 7,640 3,820 1,910 955 2,866 1,433

More profiles

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