561,906

2 × 3² × 19 × 31 × 53

561,906 factors as 2 × 3^2 × 19 × 31 × 53. Its 48 positive divisors give a proper-divisor sum of 785,934, so this integer is abundant. The Collatz stopping time is 252 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 19 × 31 × 53

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,347,840

Proper Divisor Sum 785,934

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #561839 ← → #561907

Radix Representation

Decimal	561906
Binary	10001001001011110010 (20 bits)
Octal	0o2111362
Hexadecimal	0x892F2

Divisor Catalog (48)

1 2 3 6 9 18 19 31 38 53 57 62 93 106 114 159 171 186 279 318 342 477 558 589 954 1,007 1,178 1,643 1,767 2,014 3,021 3,286 3,534 4,929 5,301 6,042 9,063 9,858 10,602 14,787 18,126 29,574 31,217 62,434 93,651 187,302 280,953 561,906

Collatz Trajectory (252 steps to reach 1)

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

561,906 280,953 842,860 421,430 210,715 632,146 316,073 948,220 474,110 237,055 711,166 355,583 1,066,750 533,375 1,600,126 800,063 2,400,190 1,200,095 3,600,286 1,800,143 5,400,430 2,700,215 8,100,646 4,050,323 12,150,970 6,075,485 18,226,456 9,113,228 4,556,614 2,278,307 6,834,922 3,417,461 10,252,384 5,126,192 2,563,096 1,281,548 640,774 320,387 961,162 480,581 1,441,744 720,872 360,436 180,218 90,109 270,328 135,164 67,582 33,791 101,374 50,687 152,062 76,031 228,094 114,047 342,142 171,071 513,214 256,607 769,822

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