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Atlas › Integer Profiles › Node 2,129,085

2,129,085

34 × 5 × 7 × 751
Abundant Odd Composite

2,129,085 factors as 3^4 × 5 × 7 × 751. Its 40 positive divisors give a proper-divisor sum of 2,238,531, so this integer is abundant. The Collatz stopping time is 210 steps.

Prime Factor Structure

Factorization String 3^4 × 5 × 7 × 751
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 4,367,616
Proper Divisor Sum 2,238,531
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #2129069 ← → #2129107

Radix Representation

Decimal 2129085
Binary 1000000111110010111101 (22 bits)
Octal 0o10076275
Hexadecimal 0x207CBD

Divisor Catalog (40)

1 3 5 7 9 15 21 27 35 45 63 81 105 135 189 315 405 567 751 945 2,253 2,835 3,755 5,257 6,759 11,265 15,771 20,277 26,285 33,795 47,313 60,831 78,855 101,385 141,939 236,565 304,155 425,817 709,695 2,129,085

Collatz Trajectory (210 steps to reach 1)

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

2,129,085 6,387,256 3,193,628 1,596,814 798,407 2,395,222 1,197,611 3,592,834 1,796,417 5,389,252 2,694,626 1,347,313 4,041,940 2,020,970 1,010,485 3,031,456 1,515,728 757,864 378,932 189,466 94,733 284,200 142,100 71,050 35,525 106,576 53,288 26,644 13,322 6,661 19,984 9,992 4,996 2,498 1,249 3,748 1,874 937 2,812 1,406 703 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511 13,534

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