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Atlas › Integer Profiles › Node 1,027,134

1,027,134

2 × 33 × 23 × 827
Abundant Even Composite

1,027,134 factors as 2 × 3^3 × 23 × 827. Its 32 positive divisors give a proper-divisor sum of 1,357,506, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 23 × 827
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 2,384,640
Proper Divisor Sum 1,357,506
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #1027129 ← → #1027139

Radix Representation

Decimal 1027134
Binary 11111010110000111110 (20 bits)
Octal 0o3726076
Hexadecimal 0xFAC3E

Divisor Catalog (32)

1 2 3 6 9 18 23 27 46 54 69 138 207 414 621 827 1,242 1,654 2,481 4,962 7,443 14,886 19,021 22,329 38,042 44,658 57,063 114,126 171,189 342,378 513,567 1,027,134

Collatz Trajectory (165 steps to reach 1)

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

1,027,134 513,567 1,540,702 770,351 2,311,054 1,155,527 3,466,582 1,733,291 5,199,874 2,599,937 7,799,812 3,899,906 1,949,953 5,849,860 2,924,930 1,462,465 4,387,396 2,193,698 1,096,849 3,290,548 1,645,274 822,637 2,467,912 1,233,956 616,978 308,489 925,468 462,734 231,367 694,102 347,051 1,041,154 520,577 1,561,732 780,866 390,433 1,171,300 585,650 292,825 878,476 439,238 219,619 658,858 329,429 988,288 494,144 247,072 123,536 61,768 30,884 15,442 7,721 23,164 11,582 5,791 17,374 8,687 26,062 13,031 39,094

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