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Atlas › Integer Profiles › Node 17,511,840

17,511,840

25 × 32 × 5 × 12161
Abundant Even Composite

17,511,840 factors as 2^5 × 3^2 × 5 × 12161. Its 72 positive divisors give a proper-divisor sum of 42,252,228, so this integer is abundant. The Collatz stopping time is 182 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 12161
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 59,764,068
Proper Divisor Sum 42,252,228
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #17511839 ← → #17511847

Radix Representation

Decimal 17511840
Binary 1000010110011010110100000 (25 bits)
Octal 0o102632640
Hexadecimal 0x10B35A0

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 288 360 480 720 1,440 12,161 24,322 36,483 48,644 60,805 72,966 97,288 109,449 121,610 145,932 182,415 194,576 218,898 243,220 291,864 364,830 389,152 437,796 486,440 547,245 583,728 729,660 875,592 972,880

Collatz Trajectory (182 steps to reach 1)

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

17,511,840 8,755,920 4,377,960 2,188,980 1,094,490 547,245 1,641,736 820,868 410,434 205,217 615,652 307,826 153,913 461,740 230,870 115,435 346,306 173,153 519,460 259,730 129,865 389,596 194,798 97,399 292,198 146,099 438,298 219,149 657,448 328,724 164,362 82,181 246,544 123,272 61,636 30,818 15,409 46,228 23,114 11,557 34,672 17,336 8,668 4,334 2,167 6,502 3,251 9,754 4,877 14,632 7,316 3,658 1,829 5,488 2,744 1,372 686 343 1,030 515

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