405,390

2 × 3 × 5 × 13513

Starting at 405,390, the Collatz iteration reaches 1 after 192 steps. The first transition is 202695; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 13513

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 973,008

Proper Divisor Sum 567,618

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #405373 ← → #405401

Radix Representation

Decimal	405390
Binary	1100010111110001110 (19 bits)
Octal	0o1427616
Hexadecimal	0x62F8E

Divisor Catalog (16)

1 2 3 5 6 10 15 30 13,513 27,026 40,539 67,565 81,078 135,130 202,695 405,390

Collatz Trajectory (192 steps to reach 1)

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

405,390 202,695 608,086 304,043 912,130 456,065 1,368,196 684,098 342,049 1,026,148 513,074 256,537 769,612 384,806 192,403 577,210 288,605 865,816 432,908 216,454 108,227 324,682 162,341 487,024 243,512 121,756 60,878 30,439 91,318 45,659 136,978 68,489 205,468 102,734 51,367 154,102 77,051 231,154 115,577 346,732 173,366 86,683 260,050 130,025 390,076 195,038 97,519 292,558 146,279 438,838 219,419 658,258 329,129 987,388 493,694 246,847 740,542 370,271 1,110,814 555,407

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