507,105

3² × 5 × 59 × 191

Starting at 507,105, the Collatz iteration reaches 1 after 107 steps. The first transition is 1521316; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5 × 59 × 191

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 898,560

Proper Divisor Sum 391,455

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #507103 ← → #507109

Radix Representation

Decimal	507105
Binary	1111011110011100001 (19 bits)
Octal	0o1736341
Hexadecimal	0x7BCE1

Divisor Catalog (24)

1 3 5 9 15 45 59 177 191 295 531 573 885 955 1,719 2,655 2,865 8,595 11,269 33,807 56,345 101,421 169,035 507,105

Collatz Trajectory (107 steps to reach 1)

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

507,105 1,521,316 760,658 380,329 1,140,988 570,494 285,247 855,742 427,871 1,283,614 641,807 1,925,422 962,711 2,888,134 1,444,067 4,332,202 2,166,101 6,498,304 3,249,152 1,624,576 812,288 406,144 203,072 101,536 50,768 25,384 12,692 6,346 3,173 9,520 4,760 2,380 1,190 595 1,786 893 2,680 1,340 670 335 1,006 503 1,510 755 2,266 1,133 3,400 1,700 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238

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