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Atlas › Integer Profiles › Node 2,133,756

2,133,756

22 × 33 × 23 × 859
Abundant Even Composite

2,133,756 factors as 2^2 × 3^3 × 23 × 859. Its 48 positive divisors give a proper-divisor sum of 3,645,444, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 23 × 859
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 5,779,200
Proper Divisor Sum 3,645,444
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #2133743 ← → #2133773

Radix Representation

Decimal 2133756
Binary 1000001000111011111100 (22 bits)
Octal 0o10107374
Hexadecimal 0x208EFC

Divisor Catalog (48)

1 2 3 4 6 9 12 18 23 27 36 46 54 69 92 108 138 207 276 414 621 828 859 1,242 1,718 2,484 2,577 3,436 5,154 7,731 10,308 15,462 19,757 23,193 30,924 39,514 46,386 59,271 79,028 92,772 118,542 177,813 237,084 355,626 533,439 711,252 1,066,878 2,133,756

Collatz Trajectory (166 steps to reach 1)

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

2,133,756 1,066,878 533,439 1,600,318 800,159 2,400,478 1,200,239 3,600,718 1,800,359 5,401,078 2,700,539 8,101,618 4,050,809 12,152,428 6,076,214 3,038,107 9,114,322 4,557,161 13,671,484 6,835,742 3,417,871 10,253,614 5,126,807 15,380,422 7,690,211 23,070,634 11,535,317 34,605,952 17,302,976 8,651,488 4,325,744 2,162,872 1,081,436 540,718 270,359 811,078 405,539 1,216,618 608,309 1,824,928 912,464 456,232 228,116 114,058 57,029 171,088 85,544 42,772 21,386 10,693 32,080 16,040 8,020 4,010 2,005 6,016 3,008 1,504 752 376

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