λ
Harmonic Matrix

9,142,092

22 × 33 × 84649
Abundant Even Composite

9,142,092 has digital root 9. The neighboring primes are 9142087 and 9142093; its proper-divisor sum differs from the starting integer by 5,417,816.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 84649
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 23,702,000
Proper Divisor Sum 14,559,908
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #9142087 ← → #9142093

Radix Representation

Decimal 9142092
Binary 100010110111111101001100 (24 bits)
Octal 0o42677514
Hexadecimal 0x8B7F4C

Divisor Catalog (24)

1 2 3 4 6 9 12 18 27 36 54 108 84,649 169,298 253,947 338,596 507,894 761,841 1,015,788 1,523,682 2,285,523 3,047,364 4,571,046 9,142,092

Collatz Trajectory (80 steps to reach 1)

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

9,142,092 4,571,046 2,285,523 6,856,570 3,428,285 10,284,856 5,142,428 2,571,214 1,285,607 3,856,822 1,928,411 5,785,234 2,892,617 8,677,852 4,338,926 2,169,463 6,508,390 3,254,195 9,762,586 4,881,293 14,643,880 7,321,940 3,660,970 1,830,485 5,491,456 2,745,728 1,372,864 686,432 343,216 171,608 85,804 42,902 21,451 64,354 32,177 96,532 48,266 24,133 72,400 36,200 18,100 9,050 4,525 13,576 6,788 3,394 1,697 5,092 2,546 1,273 3,820 1,910 955 2,866 1,433 4,300 2,150 1,075 3,226 1,613

More profiles

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