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Atlas › Integer Profiles › Node 6,137,586

6,137,586

2 × 33 × 7 × 13 × 1249
Abundant Even Composite

6,137,586 factors as 2 × 3^3 × 7 × 13 × 1249. Its 64 positive divisors give a proper-divisor sum of 10,662,414, so this integer is abundant. The Collatz stopping time is 103 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 7 × 13 × 1249
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 16,800,000
Proper Divisor Sum 10,662,414
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #6137569 ← → #6137587

Radix Representation

Decimal 6137586
Binary 10111011010011011110010 (23 bits)
Octal 0o27323362
Hexadecimal 0x5DA6F2

Divisor Catalog (60 of 64)

1 2 3 6 7 9 13 14 18 21 26 27 39 42 54 63 78 91 117 126 182 189 234 273 351 378 546 702 819 1,249 1,638 2,457 2,498 3,747 4,914 7,494 8,743 11,241 16,237 17,486 22,482 26,229 32,474 33,723 48,711 52,458 67,446 78,687 97,422 113,659 146,133 157,374 227,318 236,061 292,266 340,977 438,399 472,122 681,954 876,798

Collatz Trajectory (103 steps to reach 1)

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

6,137,586 3,068,793 9,206,380 4,603,190 2,301,595 6,904,786 3,452,393 10,357,180 5,178,590 2,589,295 7,767,886 3,883,943 11,651,830 5,825,915 17,477,746 8,738,873 26,216,620 13,108,310 6,554,155 19,662,466 9,831,233 29,493,700 14,746,850 7,373,425 22,120,276 11,060,138 5,530,069 16,590,208 8,295,104 4,147,552 2,073,776 1,036,888 518,444 259,222 129,611 388,834 194,417 583,252 291,626 145,813 437,440 218,720 109,360 54,680 27,340 13,670 6,835 20,506 10,253 30,760 15,380 7,690 3,845 11,536 5,768 2,884 1,442 721 2,164 1,082

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