λ
Harmonic Matrix

3,197,052

22 × 32 × 88807
Abundant Even Composite

3,197,052 has digital root 9. The neighboring primes are 3197027 and 3197063; its proper-divisor sum differs from the starting integer by 1,687,424.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 88807
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 18
Divisor Sum (σ) 8,081,528
Proper Divisor Sum 4,884,476
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #3197027 ← → #3197063

Radix Representation

Decimal 3197052
Binary 1100001100100001111100 (22 bits)
Octal 0o14144174
Hexadecimal 0x30C87C

Divisor Catalog (18)

1 2 3 4 6 9 12 18 36 88,807 177,614 266,421 355,228 532,842 799,263 1,065,684 1,598,526 3,197,052

Collatz Trajectory (102 steps to reach 1)

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

3,197,052 1,598,526 799,263 2,397,790 1,198,895 3,596,686 1,798,343 5,395,030 2,697,515 8,092,546 4,046,273 12,138,820 6,069,410 3,034,705 9,104,116 4,552,058 2,276,029 6,828,088 3,414,044 1,707,022 853,511 2,560,534 1,280,267 3,840,802 1,920,401 5,761,204 2,880,602 1,440,301 4,320,904 2,160,452 1,080,226 540,113 1,620,340 810,170 405,085 1,215,256 607,628 303,814 151,907 455,722 227,861 683,584 341,792 170,896 85,448 42,724 21,362 10,681 32,044 16,022 8,011 24,034 12,017 36,052 18,026 9,013 27,040 13,520 6,760 3,380

More profiles

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