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Atlas › Integer Profiles › Node 3,221,800

3,221,800

23 × 52 × 89 × 181
Abundant Even Composite

3,221,800 factors as 2^3 × 5^2 × 89 × 181. Its 48 positive divisors give a proper-divisor sum of 4,394,900, so this integer is abundant. The Collatz stopping time is 270 steps.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 89 × 181
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 7,616,700
Proper Divisor Sum 4,394,900
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #3221791 ← → #3221807

Radix Representation

Decimal 3221800
Binary 1100010010100100101000 (22 bits)
Octal 0o14224450
Hexadecimal 0x312928

Divisor Catalog (48)

1 2 4 5 8 10 20 25 40 50 89 100 178 181 200 356 362 445 712 724 890 905 1,448 1,780 1,810 2,225 3,560 3,620 4,450 4,525 7,240 8,900 9,050 16,109 17,800 18,100 32,218 36,200 64,436 80,545 128,872 161,090 322,180 402,725 644,360 805,450 1,610,900 3,221,800

Collatz Trajectory (270 steps to reach 1)

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

3,221,800 1,610,900 805,450 402,725 1,208,176 604,088 302,044 151,022 75,511 226,534 113,267 339,802 169,901 509,704 254,852 127,426 63,713 191,140 95,570 47,785 143,356 71,678 35,839 107,518 53,759 161,278 80,639 241,918 120,959 362,878 181,439 544,318 272,159 816,478 408,239 1,224,718 612,359 1,837,078 918,539 2,755,618 1,377,809 4,133,428 2,066,714 1,033,357 3,100,072 1,550,036 775,018 387,509 1,162,528 581,264 290,632 145,316 72,658 36,329 108,988 54,494 27,247 81,742 40,871 122,614

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