λ
Harmonic Matrix

8,563,041

32 × 951449
Deficient Odd Composite

8,563,041 has digital root 9. The neighboring primes are 8563039 and 8563043; its proper-divisor sum differs from the starting integer by -4,757,232.

Prime Factor Structure

Factorization String 3^2 × 951449
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 6
Divisor Sum (σ) 12,368,850
Proper Divisor Sum 3,805,809
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8563039 ← → #8563043

Radix Representation

Decimal 8563041
Binary 100000101010100101100001 (24 bits)
Octal 0o40524541
Hexadecimal 0x82A961

Divisor Catalog (6)

1 3 9 951,449 2,854,347 8,563,041

Collatz Trajectory (150 steps to reach 1)

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

8,563,041 25,689,124 12,844,562 6,422,281 19,266,844 9,633,422 4,816,711 14,450,134 7,225,067 21,675,202 10,837,601 32,512,804 16,256,402 8,128,201 24,384,604 12,192,302 6,096,151 18,288,454 9,144,227 27,432,682 13,716,341 41,149,024 20,574,512 10,287,256 5,143,628 2,571,814 1,285,907 3,857,722 1,928,861 5,786,584 2,893,292 1,446,646 723,323 2,169,970 1,084,985 3,254,956 1,627,478 813,739 2,441,218 1,220,609 3,661,828 1,830,914 915,457 2,746,372 1,373,186 686,593 2,059,780 1,029,890 514,945 1,544,836 772,418 386,209 1,158,628 579,314 289,657 868,972 434,486 217,243 651,730 325,865

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