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Atlas › Integer Profiles › Node 6,137,628

6,137,628

22 × 3 × 7 × 31 × 2357
Abundant Even Composite

6,137,628 factors as 2^2 × 3 × 7 × 31 × 2357. Its 48 positive divisors give a proper-divisor sum of 10,764,516, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 31 × 2357
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 16,902,144
Proper Divisor Sum 10,764,516
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #6137623 ← → #6137633

Radix Representation

Decimal 6137628
Binary 10111011010011100011100 (23 bits)
Octal 0o27323434
Hexadecimal 0x5DA71C

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 31 42 62 84 93 124 186 217 372 434 651 868 1,302 2,357 2,604 4,714 7,071 9,428 14,142 16,499 28,284 32,998 49,497 65,996 73,067 98,994 146,134 197,988 219,201 292,268 438,402 511,469 876,804 1,022,938 1,534,407 2,045,876 3,068,814 6,137,628

Collatz Trajectory (196 steps to reach 1)

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

6,137,628 3,068,814 1,534,407 4,603,222 2,301,611 6,904,834 3,452,417 10,357,252 5,178,626 2,589,313 7,767,940 3,883,970 1,941,985 5,825,956 2,912,978 1,456,489 4,369,468 2,184,734 1,092,367 3,277,102 1,638,551 4,915,654 2,457,827 7,373,482 3,686,741 11,060,224 5,530,112 2,765,056 1,382,528 691,264 345,632 172,816 86,408 43,204 21,602 10,801 32,404 16,202 8,101 24,304 12,152 6,076 3,038 1,519 4,558 2,279 6,838 3,419 10,258 5,129 15,388 7,694 3,847 11,542 5,771 17,314 8,657 25,972 12,986 6,493

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