414,491

7² × 11 × 769

414,491 has the prime decomposition 7^2 × 11 × 769. Its 3 distinct prime factors produce 12 positive divisors.

Prime Factor Structure

Factorization String 7^2 × 11 × 769

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 526,680

Proper Divisor Sum 112,189

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #414487 ← → #414503

Radix Representation

Decimal	414491
Binary	1100101001100011011 (19 bits)
Octal	0o1451433
Hexadecimal	0x6531B

Divisor Catalog (12)

1 7 11 49 77 539 769 5,383 8,459 37,681 59,213 414,491

Collatz Trajectory (112 steps to reach 1)

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

414,491 1,243,474 621,737 1,865,212 932,606 466,303 1,398,910 699,455 2,098,366 1,049,183 3,147,550 1,573,775 4,721,326 2,360,663 7,081,990 3,540,995 10,622,986 5,311,493 15,934,480 7,967,240 3,983,620 1,991,810 995,905 2,987,716 1,493,858 746,929 2,240,788 1,120,394 560,197 1,680,592 840,296 420,148 210,074 105,037 315,112 157,556 78,778 39,389 118,168 59,084 29,542 14,771 44,314 22,157 66,472 33,236 16,618 8,309 24,928 12,464 6,232 3,116 1,558 779 2,338 1,169 3,508 1,754 877 2,632

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