λ
Harmonic Matrix

8,501,005

5 × 233 × 7297
Deficient Odd Composite

8,501,005 has digital root 1. The neighboring primes are 8500967 and 8501011; its proper-divisor sum differs from the starting integer by -6,755,618.

Prime Factor Structure

Factorization String 5 × 233 × 7297
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 10,246,392
Proper Divisor Sum 1,745,387
Digit Sum / Digital Root 19 (Root: 1)
Adjacent Primes #8500967 ← → #8501011

Radix Representation

Decimal 8501005
Binary 100000011011011100001101 (24 bits)
Octal 0o40333415
Hexadecimal 0x81B70D

Divisor Catalog (8)

1 5 233 1,165 7,297 36,485 1,700,201 8,501,005

Collatz Trajectory (150 steps to reach 1)

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

8,501,005 25,503,016 12,751,508 6,375,754 3,187,877 9,563,632 4,781,816 2,390,908 1,195,454 597,727 1,793,182 896,591 2,689,774 1,344,887 4,034,662 2,017,331 6,051,994 3,025,997 9,077,992 4,538,996 2,269,498 1,134,749 3,404,248 1,702,124 851,062 425,531 1,276,594 638,297 1,914,892 957,446 478,723 1,436,170 718,085 2,154,256 1,077,128 538,564 269,282 134,641 403,924 201,962 100,981 302,944 151,472 75,736 37,868 18,934 9,467 28,402 14,201 42,604 21,302 10,651 31,954 15,977 47,932 23,966 11,983 35,950 17,975 53,926

More profiles

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