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Atlas › Integer Profiles › Node 27,408,568

27,408,568

23 × 11 × 59 × 5279
Abundant Even Composite

27,408,568 factors as 2^3 × 11 × 59 × 5279. Its 32 positive divisors give a proper-divisor sum of 29,615,432, so this integer is abundant. The Collatz stopping time is 162 steps.

Prime Factor Structure

Factorization String 2^3 × 11 × 59 × 5279
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 57,024,000
Proper Divisor Sum 29,615,432
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #27408559 ← → #27408593

Radix Representation

Decimal 27408568
Binary 1101000100011100010111000 (25 bits)
Octal 0o150434270
Hexadecimal 0x1A238B8

Divisor Catalog (32)

1 2 4 8 11 22 44 59 88 118 236 472 649 1,298 2,596 5,192 5,279 10,558 21,116 42,232 58,069 116,138 232,276 311,461 464,552 622,922 1,245,844 2,491,688 3,426,071 6,852,142 13,704,284 27,408,568

Collatz Trajectory (162 steps to reach 1)

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

27,408,568 13,704,284 6,852,142 3,426,071 10,278,214 5,139,107 15,417,322 7,708,661 23,125,984 11,562,992 5,781,496 2,890,748 1,445,374 722,687 2,168,062 1,084,031 3,252,094 1,626,047 4,878,142 2,439,071 7,317,214 3,658,607 10,975,822 5,487,911 16,463,734 8,231,867 24,695,602 12,347,801 37,043,404 18,521,702 9,260,851 27,782,554 13,891,277 41,673,832 20,836,916 10,418,458 5,209,229 15,627,688 7,813,844 3,906,922 1,953,461 5,860,384 2,930,192 1,465,096 732,548 366,274 183,137 549,412 274,706 137,353 412,060 206,030 103,015 309,046 154,523 463,570 231,785 695,356 347,678 173,839

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