504,114

2 × 3 × 13 × 23 × 281

Starting at 504,114, the Collatz iteration reaches 1 after 89 steps. The first transition is 252057; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 23 × 281

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,137,024

Proper Divisor Sum 632,910

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #504103 ← → #504121

Radix Representation

Decimal	504114
Binary	1111011000100110010 (19 bits)
Octal	0o1730462
Hexadecimal	0x7B132

Divisor Catalog (32)

1 2 3 6 13 23 26 39 46 69 78 138 281 299 562 598 843 897 1,686 1,794 3,653 6,463 7,306 10,959 12,926 19,389 21,918 38,778 84,019 168,038 252,057 504,114

Collatz Trajectory (89 steps to reach 1)

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

504,114 252,057 756,172 378,086 189,043 567,130 283,565 850,696 425,348 212,674 106,337 319,012 159,506 79,753 239,260 119,630 59,815 179,446 89,723 269,170 134,585 403,756 201,878 100,939 302,818 151,409 454,228 227,114 113,557 340,672 170,336 85,168 42,584 21,292 10,646 5,323 15,970 7,985 23,956 11,978 5,989 17,968 8,984 4,492 2,246 1,123 3,370 1,685 5,056 2,528 1,264 632 316 158 79 238 119 358 179 538

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