65,655

3² × 5 × 1459

Starting at 65,655, the Collatz iteration reaches 1 after 99 steps. The first transition is 196966; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5 × 1459

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 113,880

Proper Divisor Sum 48,225

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #65651 ← → #65657

Radix Representation

Decimal	65655
Binary	10000000001110111 (17 bits)
Octal	0o200167
Hexadecimal	0x10077

Divisor Catalog (12)

1 3 5 9 15 45 1,459 4,377 7,295 13,131 21,885 65,655

Collatz Trajectory (99 steps to reach 1)

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

65,655 196,966 98,483 295,450 147,725 443,176 221,588 110,794 55,397 166,192 83,096 41,548 20,774 10,387 31,162 15,581 46,744 23,372 11,686 5,843 17,530 8,765 26,296 13,148 6,574 3,287 9,862 4,931 14,794 7,397 22,192 11,096 5,548 2,774 1,387 4,162 2,081 6,244 3,122 1,561 4,684 2,342 1,171 3,514 1,757 5,272 2,636 1,318 659 1,978 989 2,968 1,484 742 371 1,114 557 1,672 836 418

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