726,009

3 × 19 × 47 × 271

Starting at 726,009, the Collatz iteration reaches 1 after 118 steps. The first transition is 2178028; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 19 × 47 × 271

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,044,480

Proper Divisor Sum 318,471

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #726007 ← → #726013

Radix Representation

Decimal	726009
Binary	10110001001111111001 (20 bits)
Octal	0o2611771
Hexadecimal	0xB13F9

Divisor Catalog (16)

1 3 19 47 57 141 271 813 893 2,679 5,149 12,737 15,447 38,211 242,003 726,009

Collatz Trajectory (118 steps to reach 1)

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

726,009 2,178,028 1,089,014 544,507 1,633,522 816,761 2,450,284 1,225,142 612,571 1,837,714 918,857 2,756,572 1,378,286 689,143 2,067,430 1,033,715 3,101,146 1,550,573 4,651,720 2,325,860 1,162,930 581,465 1,744,396 872,198 436,099 1,308,298 654,149 1,962,448 981,224 490,612 245,306 122,653 367,960 183,980 91,990 45,995 137,986 68,993 206,980 103,490 51,745 155,236 77,618 38,809 116,428 58,214 29,107 87,322 43,661 130,984 65,492 32,746 16,373 49,120 24,560 12,280 6,140 3,070 1,535 4,606

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