λ
Harmonic Matrix

207,140

22 × 5 × 10357
Abundant Even Composite

207,140 has digital root 5. The neighboring primes are 207139 and 207169; its proper-divisor sum differs from the starting integer by 20,756.

Prime Factor Structure

Factorization String 2^2 × 5 × 10357
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 435,036
Proper Divisor Sum 227,896
Digit Sum / Digital Root 14 (Root: 5)
Adjacent Primes #207139 ← → #207169

Radix Representation

Decimal 207140
Binary 110010100100100100 (18 bits)
Octal 0o624444
Hexadecimal 0x32924

Divisor Catalog (12)

1 2 4 5 10 20 10,357 20,714 41,428 51,785 103,570 207,140

Collatz Trajectory (67 steps to reach 1)

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

207,140 103,570 51,785 155,356 77,678 38,839 116,518 58,259 174,778 87,389 262,168 131,084 65,542 32,771 98,314 49,157 147,472 73,736 36,868 18,434 9,217 27,652 13,826 6,913 20,740 10,370 5,185 15,556 7,778 3,889 11,668 5,834 2,917 8,752 4,376 2,188 1,094 547 1,642 821 2,464 1,232 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40

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