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Atlas › Integer Profiles › Node 22,509,220

22,509,220

22 × 5 × 29 × 1972
Abundant Even Composite

22,509,220 factors as 2^2 × 5 × 29 × 197^2. Its 36 positive divisors give a proper-divisor sum of 26,639,600, so this integer is abundant. The Collatz stopping time is 133 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 29 × 197^2
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 49,148,820
Proper Divisor Sum 26,639,600
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #22509217 ← → #22509229

Radix Representation

Decimal 22509220
Binary 1010101110111011010100100 (25 bits)
Octal 0o125673244
Hexadecimal 0x15776A4

Divisor Catalog (36)

1 2 4 5 10 20 29 58 116 145 197 290 394 580 788 985 1,970 3,940 5,713 11,426 22,852 28,565 38,809 57,130 77,618 114,260 155,236 194,045 388,090 776,180 1,125,461 2,250,922 4,501,844 5,627,305 11,254,610 22,509,220

Collatz Trajectory (133 steps to reach 1)

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

22,509,220 11,254,610 5,627,305 16,881,916 8,440,958 4,220,479 12,661,438 6,330,719 18,992,158 9,496,079 28,488,238 14,244,119 42,732,358 21,366,179 64,098,538 32,049,269 96,147,808 48,073,904 24,036,952 12,018,476 6,009,238 3,004,619 9,013,858 4,506,929 13,520,788 6,760,394 3,380,197 10,140,592 5,070,296 2,535,148 1,267,574 633,787 1,901,362 950,681 2,852,044 1,426,022 713,011 2,139,034 1,069,517 3,208,552 1,604,276 802,138 401,069 1,203,208 601,604 300,802 150,401 451,204 225,602 112,801 338,404 169,202 84,601 253,804 126,902 63,451 190,354 95,177 285,532 142,766

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