λ
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Atlas › Integer Profiles › Node 1,027,608

1,027,608

23 × 3 × 47 × 911
Abundant Even Composite

1,027,608 factors as 2^3 × 3 × 47 × 911. Its 32 positive divisors give a proper-divisor sum of 1,598,952, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 47 × 911
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 2,626,560
Proper Divisor Sum 1,598,952
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #1027597 ← → #1027613

Radix Representation

Decimal 1027608
Binary 11111010111000011000 (20 bits)
Octal 0o3727030
Hexadecimal 0xFAE18

Divisor Catalog (32)

1 2 3 4 6 8 12 24 47 94 141 188 282 376 564 911 1,128 1,822 2,733 3,644 5,466 7,288 10,932 21,864 42,817 85,634 128,451 171,268 256,902 342,536 513,804 1,027,608

Collatz Trajectory (196 steps to reach 1)

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

1,027,608 513,804 256,902 128,451 385,354 192,677 578,032 289,016 144,508 72,254 36,127 108,382 54,191 162,574 81,287 243,862 121,931 365,794 182,897 548,692 274,346 137,173 411,520 205,760 102,880 51,440 25,720 12,860 6,430 3,215 9,646 4,823 14,470 7,235 21,706 10,853 32,560 16,280 8,140 4,070 2,035 6,106 3,053 9,160 4,580 2,290 1,145 3,436 1,718 859 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532

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