405,576

2³ × 3² × 43 × 131

405,576 factors as 2^3 × 3^2 × 43 × 131. Its 48 positive divisors give a proper-divisor sum of 726,984, so this integer is abundant. The Collatz stopping time is 117 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 43 × 131

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,132,560

Proper Divisor Sum 726,984

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #405553 ← → #405577

Radix Representation

Decimal	405576
Binary	1100011000001001000 (19 bits)
Octal	0o1430110
Hexadecimal	0x63048

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 43 72 86 129 131 172 258 262 344 387 393 516 524 774 786 1,032 1,048 1,179 1,548 1,572 2,358 3,096 3,144 4,716 5,633 9,432 11,266 16,899 22,532 33,798 45,064 50,697 67,596 101,394 135,192 202,788 405,576

Collatz Trajectory (117 steps to reach 1)

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

405,576 202,788 101,394 50,697 152,092 76,046 38,023 114,070 57,035 171,106 85,553 256,660 128,330 64,165 192,496 96,248 48,124 24,062 12,031 36,094 18,047 54,142 27,071 81,214 40,607 121,822 60,911 182,734 91,367 274,102 137,051 411,154 205,577 616,732 308,366 154,183 462,550 231,275 693,826 346,913 1,040,740 520,370 260,185 780,556 390,278 195,139 585,418 292,709 878,128 439,064 219,532 109,766 54,883 164,650 82,325 246,976 123,488 61,744 30,872 15,436

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