513,052

2² × 47 × 2729

Starting at 513,052, the Collatz iteration reaches 1 after 187 steps. The first transition is 256526; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 47 × 2729

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 917,280

Proper Divisor Sum 404,228

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #513047 ← → #513053

Radix Representation

Decimal	513052
Binary	1111101010000011100 (19 bits)
Octal	0o1752034
Hexadecimal	0x7D41C

Divisor Catalog (12)

1 2 4 47 94 188 2,729 5,458 10,916 128,263 256,526 513,052

Collatz Trajectory (187 steps to reach 1)

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

513,052 256,526 128,263 384,790 192,395 577,186 288,593 865,780 432,890 216,445 649,336 324,668 162,334 81,167 243,502 121,751 365,254 182,627 547,882 273,941 821,824 410,912 205,456 102,728 51,364 25,682 12,841 38,524 19,262 9,631 28,894 14,447 43,342 21,671 65,014 32,507 97,522 48,761 146,284 73,142 36,571 109,714 54,857 164,572 82,286 41,143 123,430 61,715 185,146 92,573 277,720 138,860 69,430 34,715 104,146 52,073 156,220 78,110 39,055 117,166

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