688,575

3 × 5² × 9181

Starting at 688,575, the Collatz iteration reaches 1 after 92 steps. The first transition is 2065726; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 9181

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,138,568

Proper Divisor Sum 449,993

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #688573 ← → #688591

Radix Representation

Decimal	688575
Binary	10101000000110111111 (20 bits)
Octal	0o2500677
Hexadecimal	0xA81BF

Divisor Catalog (12)

1 3 5 15 25 75 9,181 27,543 45,905 137,715 229,525 688,575

Collatz Trajectory (92 steps to reach 1)

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

688,575 2,065,726 1,032,863 3,098,590 1,549,295 4,647,886 2,323,943 6,971,830 3,485,915 10,457,746 5,228,873 15,686,620 7,843,310 3,921,655 11,764,966 5,882,483 17,647,450 8,823,725 26,471,176 13,235,588 6,617,794 3,308,897 9,926,692 4,963,346 2,481,673 7,445,020 3,722,510 1,861,255 5,583,766 2,791,883 8,375,650 4,187,825 12,563,476 6,281,738 3,140,869 9,422,608 4,711,304 2,355,652 1,177,826 588,913 1,766,740 883,370 441,685 1,325,056 662,528 331,264 165,632 82,816 41,408 20,704 10,352 5,176 2,588 1,294 647 1,942 971 2,914 1,457 4,372

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