4,657,401

3² × 7² × 59 × 179

Starting at 4,657,401, the Collatz iteration reaches 1 after 131 steps. The first transition is 13972204; the starting value is odd with 36 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 7^2 × 59 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 8,002,800

Proper Divisor Sum 3,345,399

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #4657397 ← → #4657417

Radix Representation

Decimal	4657401
Binary	10001110001000011111001 (23 bits)
Octal	0o21610371
Hexadecimal	0x4710F9

Divisor Catalog (36)

1 3 7 9 21 49 59 63 147 177 179 413 441 531 537 1,239 1,253 1,611 2,891 3,717 3,759 8,673 8,771 10,561 11,277 26,019 26,313 31,683 73,927 78,939 95,049 221,781 517,489 665,343 1,552,467 4,657,401

Collatz Trajectory (131 steps to reach 1)

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

4,657,401 13,972,204 6,986,102 3,493,051 10,479,154 5,239,577 15,718,732 7,859,366 3,929,683 11,789,050 5,894,525 17,683,576 8,841,788 4,420,894 2,210,447 6,631,342 3,315,671 9,947,014 4,973,507 14,920,522 7,460,261 22,380,784 11,190,392 5,595,196 2,797,598 1,398,799 4,196,398 2,098,199 6,294,598 3,147,299 9,441,898 4,720,949 14,162,848 7,081,424 3,540,712 1,770,356 885,178 442,589 1,327,768 663,884 331,942 165,971 497,914 248,957 746,872 373,436 186,718 93,359 280,078 140,039 420,118 210,059 630,178 315,089 945,268 472,634 236,317 708,952 354,476 177,238

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