415,635

3 × 5 × 11² × 229

Starting at 415,635, the Collatz iteration reaches 1 after 174 steps. The first transition is 1246906; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 11^2 × 229

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 734,160

Proper Divisor Sum 318,525

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #415631 ← → #415643

Radix Representation

Decimal	415635
Binary	1100101011110010011 (19 bits)
Octal	0o1453623
Hexadecimal	0x65793

Divisor Catalog (24)

1 3 5 11 15 33 55 121 165 229 363 605 687 1,145 1,815 2,519 3,435 7,557 12,595 27,709 37,785 83,127 138,545 415,635

Collatz Trajectory (174 steps to reach 1)

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

415,635 1,246,906 623,453 1,870,360 935,180 467,590 233,795 701,386 350,693 1,052,080 526,040 263,020 131,510 65,755 197,266 98,633 295,900 147,950 73,975 221,926 110,963 332,890 166,445 499,336 249,668 124,834 62,417 187,252 93,626 46,813 140,440 70,220 35,110 17,555 52,666 26,333 79,000 39,500 19,750 9,875 29,626 14,813 44,440 22,220 11,110 5,555 16,666 8,333 25,000 12,500 6,250 3,125 9,376 4,688 2,344 1,172 586 293 880 440

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