17,632

2⁵ × 19 × 29

Starting at 17,632, the Collatz iteration reaches 1 after 48 steps. The first transition is 8816; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 19 × 29

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 37,800

Proper Divisor Sum 20,168

Digit Sum / Digital Root 19 (Root: 1)

Adjacent Primes #17627 ← → #17657

Radix Representation

Decimal	17632
Binary	100010011100000 (15 bits)
Octal	0o42340
Hexadecimal	0x44E0

Divisor Catalog (24)

1 2 4 8 16 19 29 32 38 58 76 116 152 232 304 464 551 608 928 1,102 2,204 4,408 8,816 17,632

Collatz Trajectory (48 steps to reach 1)

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

17,632 8,816 4,408 2,204 1,102 551 1,654 827 2,482 1,241 3,724 1,862 931 2,794 1,397 4,192 2,096 1,048 524 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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