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Atlas › Integer Profiles › Node 1,609,072

1,609,072

24 × 19 × 67 × 79
Abundant Even Composite

1,609,072 factors as 2^4 × 19 × 67 × 79. Its 40 positive divisors give a proper-divisor sum of 1,763,728, so this integer is abundant. The Collatz stopping time is 145 steps.

Prime Factor Structure

Factorization String 2^4 × 19 × 67 × 79
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 3,372,800
Proper Divisor Sum 1,763,728
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #1609063 ← → #1609079

Radix Representation

Decimal 1609072
Binary 110001000110101110000 (21 bits)
Octal 0o6106560
Hexadecimal 0x188D70

Divisor Catalog (40)

1 2 4 8 16 19 38 67 76 79 134 152 158 268 304 316 536 632 1,072 1,264 1,273 1,501 2,546 3,002 5,092 5,293 6,004 10,184 10,586 12,008 20,368 21,172 24,016 42,344 84,688 100,567 201,134 402,268 804,536 1,609,072

Collatz Trajectory (145 steps to reach 1)

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

1,609,072 804,536 402,268 201,134 100,567 301,702 150,851 452,554 226,277 678,832 339,416 169,708 84,854 42,427 127,282 63,641 190,924 95,462 47,731 143,194 71,597 214,792 107,396 53,698 26,849 80,548 40,274 20,137 60,412 30,206 15,103 45,310 22,655 67,966 33,983 101,950 50,975 152,926 76,463 229,390 114,695 344,086 172,043 516,130 258,065 774,196 387,098 193,549 580,648 290,324 145,162 72,581 217,744 108,872 54,436 27,218 13,609 40,828 20,414 10,207

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