205,975

5² × 7 × 11 × 107

Starting at 205,975, the Collatz iteration reaches 1 after 111 steps. The first transition is 617926; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 7 × 11 × 107

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 321,408

Proper Divisor Sum 115,433

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #205967 ← → #205981

Radix Representation

Decimal	205975
Binary	110010010010010111 (18 bits)
Octal	0o622227
Hexadecimal	0x32497

Divisor Catalog (24)

1 5 7 11 25 35 55 77 107 175 275 385 535 749 1,177 1,925 2,675 3,745 5,885 8,239 18,725 29,425 41,195 205,975

Collatz Trajectory (111 steps to reach 1)

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

205,975 617,926 308,963 926,890 463,445 1,390,336 695,168 347,584 173,792 86,896 43,448 21,724 10,862 5,431 16,294 8,147 24,442 12,221 36,664 18,332 9,166 4,583 13,750 6,875 20,626 10,313 30,940 15,470 7,735 23,206 11,603 34,810 17,405 52,216 26,108 13,054 6,527 19,582 9,791 29,374 14,687 44,062 22,031 66,094 33,047 99,142 49,571 148,714 74,357 223,072 111,536 55,768 27,884 13,942 6,971 20,914 10,457 31,372 15,686 7,843

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