512,705

5 × 41² × 61

Starting at 512,705, the Collatz iteration reaches 1 after 76 steps. The first transition is 1538116; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 5 × 41^2 × 61

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 640,956

Proper Divisor Sum 128,251

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #512683 ← → #512711

Radix Representation

Decimal	512705
Binary	1111101001011000001 (19 bits)
Octal	0o1751301
Hexadecimal	0x7D2C1

Divisor Catalog (12)

1 5 41 61 205 305 1,681 2,501 8,405 12,505 102,541 512,705

Collatz Trajectory (76 steps to reach 1)

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

512,705 1,538,116 769,058 384,529 1,153,588 576,794 288,397 865,192 432,596 216,298 108,149 324,448 162,224 81,112 40,556 20,278 10,139 30,418 15,209 45,628 22,814 11,407 34,222 17,111 51,334 25,667 77,002 38,501 115,504 57,752 28,876 14,438 7,219 21,658 10,829 32,488 16,244 8,122 4,061 12,184 6,092 3,046 1,523 4,570 2,285 6,856 3,428 1,714 857 2,572 1,286 643 1,930 965 2,896 1,448 724 362 181 544

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