477,516

2² × 3 × 13 × 3061

Starting at 477,516, the Collatz iteration reaches 1 after 169 steps. The first transition is 238758; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 13 × 3061

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,200,304

Proper Divisor Sum 722,788

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #477511 ← → #477517

Radix Representation

Decimal	477516
Binary	1110100100101001100 (19 bits)
Octal	0o1644514
Hexadecimal	0x7494C

Divisor Catalog (24)

1 2 3 4 6 12 13 26 39 52 78 156 3,061 6,122 9,183 12,244 18,366 36,732 39,793 79,586 119,379 159,172 238,758 477,516

Collatz Trajectory (169 steps to reach 1)

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

477,516 238,758 119,379 358,138 179,069 537,208 268,604 134,302 67,151 201,454 100,727 302,182 151,091 453,274 226,637 679,912 339,956 169,978 84,989 254,968 127,484 63,742 31,871 95,614 47,807 143,422 71,711 215,134 107,567 322,702 161,351 484,054 242,027 726,082 363,041 1,089,124 544,562 272,281 816,844 408,422 204,211 612,634 306,317 918,952 459,476 229,738 114,869 344,608 172,304 86,152 43,076 21,538 10,769 32,308 16,154 8,077 24,232 12,116 6,058 3,029

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