λ
Harmonic Matrix

15,488

27 × 112
Abundant Even Composite

15,488 has digital root 8. The neighboring primes are 15473 and 15493; its proper-divisor sum differs from the starting integer by 2,939.

Prime Factor Structure

Factorization String 2^7 × 11^2
Distinct Prime Factors 2
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 33,915
Proper Divisor Sum 18,427
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #15473 ← → #15493

Radix Representation

Decimal 15488
Binary 11110010000000 (14 bits)
Octal 0o36200
Hexadecimal 0x3C80

Divisor Catalog (24)

1 2 4 8 11 16 22 32 44 64 88 121 128 176 242 352 484 704 968 1,408 1,936 3,872 7,744 15,488

Collatz Trajectory (102 steps to reach 1)

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

15,488 7,744 3,872 1,936 968 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644

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