λ
Harmonic Matrix

8,212,086

2 × 32 × 31 × 14717
Abundant Even Composite

8,212,086 has digital root 9. The neighboring primes are 8212067 and 8212091; its proper-divisor sum differs from the starting integer by 1,943,892.

Prime Factor Structure

Factorization String 2 × 3^2 × 31 × 14717
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 18,368,064
Proper Divisor Sum 10,155,978
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8212067 ← → #8212091

Radix Representation

Decimal 8212086
Binary 11111010100111001110110 (23 bits)
Octal 0o37247166
Hexadecimal 0x7D4E76

Divisor Catalog (24)

1 2 3 6 9 18 31 62 93 186 279 558 14,717 29,434 44,151 88,302 132,453 264,906 456,227 912,454 1,368,681 2,737,362 4,106,043 8,212,086

Collatz Trajectory (54 steps to reach 1)

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

8,212,086 4,106,043 12,318,130 6,159,065 18,477,196 9,238,598 4,619,299 13,857,898 6,928,949 20,786,848 10,393,424 5,196,712 2,598,356 1,299,178 649,589 1,948,768 974,384 487,192 243,596 121,798 60,899 182,698 91,349 274,048 137,024 68,512 34,256 17,128 8,564 4,282 2,141 6,424 3,212 1,606 803 2,410 1,205 3,616 1,808 904 452 226 113 340 170 85 256 128 64 32 16 8 4 2 1

More profiles

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