513,492

2² × 3 × 7 × 6113

Starting at 513,492, the Collatz iteration reaches 1 after 195 steps. The first transition is 256746; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 6113

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,369,536

Proper Divisor Sum 856,044

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #513481 ← → #513509

Radix Representation

Decimal	513492
Binary	1111101010111010100 (19 bits)
Octal	0o1752724
Hexadecimal	0x7D5D4

Divisor Catalog (24)

1 2 3 4 6 7 12 14 21 28 42 84 6,113 12,226 18,339 24,452 36,678 42,791 73,356 85,582 128,373 171,164 256,746 513,492

Collatz Trajectory (195 steps to reach 1)

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

513,492 256,746 128,373 385,120 192,560 96,280 48,140 24,070 12,035 36,106 18,053 54,160 27,080 13,540 6,770 3,385 10,156 5,078 2,539 7,618 3,809 11,428 5,714 2,857 8,572 4,286 2,143 6,430 3,215 9,646 4,823 14,470 7,235 21,706 10,853 32,560 16,280 8,140 4,070 2,035 6,106 3,053 9,160 4,580 2,290 1,145 3,436 1,718 859 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266

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