726,561

3² × 11 × 41 × 179

726,561 factors as 3^2 × 11 × 41 × 179. Its 24 positive divisors give a proper-divisor sum of 452,799, so this integer is deficient. The Collatz stopping time is 167 steps.

Prime Factor Structure

Factorization String 3^2 × 11 × 41 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,179,360

Proper Divisor Sum 452,799

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #726559 ← → #726589

Radix Representation

Decimal	726561
Binary	10110001011000100001 (20 bits)
Octal	0o2613041
Hexadecimal	0xB1621

Divisor Catalog (24)

1 3 9 11 33 41 99 123 179 369 451 537 1,353 1,611 1,969 4,059 5,907 7,339 17,721 22,017 66,051 80,729 242,187 726,561

Collatz Trajectory (167 steps to reach 1)

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

726,561 2,179,684 1,089,842 544,921 1,634,764 817,382 408,691 1,226,074 613,037 1,839,112 919,556 459,778 229,889 689,668 344,834 172,417 517,252 258,626 129,313 387,940 193,970 96,985 290,956 145,478 72,739 218,218 109,109 327,328 163,664 81,832 40,916 20,458 10,229 30,688 15,344 7,672 3,836 1,918 959 2,878 1,439 4,318 2,159 6,478 3,239 9,718 4,859 14,578 7,289 21,868 10,934 5,467 16,402 8,201 24,604 12,302 6,151 18,454 9,227 27,682

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