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Atlas › Integer Profiles › Node 2,007,456

2,007,456

25 × 3 × 11 × 1901
Abundant Even Composite

2,007,456 factors as 2^5 × 3 × 11 × 1901. Its 48 positive divisors give a proper-divisor sum of 3,744,192, so this integer is abundant. The Collatz stopping time is 60 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 11 × 1901
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 5,751,648
Proper Divisor Sum 3,744,192
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #2007451 ← → #2007487

Radix Representation

Decimal 2007456
Binary 111101010000110100000 (21 bits)
Octal 0o7520640
Hexadecimal 0x1EA1A0

Divisor Catalog (48)

1 2 3 4 6 8 11 12 16 22 24 32 33 44 48 66 88 96 132 176 264 352 528 1,056 1,901 3,802 5,703 7,604 11,406 15,208 20,911 22,812 30,416 41,822 45,624 60,832 62,733 83,644 91,248 125,466 167,288 182,496 250,932 334,576 501,864 669,152 1,003,728 2,007,456

Collatz Trajectory (60 steps to reach 1)

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

2,007,456 1,003,728 501,864 250,932 125,466 62,733 188,200 94,100 47,050 23,525 70,576 35,288 17,644 8,822 4,411 13,234 6,617 19,852 9,926 4,963 14,890 7,445 22,336 11,168 5,584 2,792 1,396 698 349 1,048 524 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2

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