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Atlas › Integer Profiles › Node 2,739,584

2,739,584

27 × 17 × 1259
Abundant Even Composite

2,739,584 factors as 2^7 × 17 × 1259. Its 32 positive divisors give a proper-divisor sum of 3,043,816, so this integer is abundant. The Collatz stopping time is 200 steps.

Prime Factor Structure

Factorization String 2^7 × 17 × 1259
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 5,783,400
Proper Divisor Sum 3,043,816
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #2739577 ← → #2739587

Radix Representation

Decimal 2739584
Binary 1010011100110110000000 (22 bits)
Octal 0o12346600
Hexadecimal 0x29CD80

Divisor Catalog (32)

1 2 4 8 16 17 32 34 64 68 128 136 272 544 1,088 1,259 2,176 2,518 5,036 10,072 20,144 21,403 40,288 42,806 80,576 85,612 161,152 171,224 342,448 684,896 1,369,792 2,739,584

Collatz Trajectory (200 steps to reach 1)

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

2,739,584 1,369,792 684,896 342,448 171,224 85,612 42,806 21,403 64,210 32,105 96,316 48,158 24,079 72,238 36,119 108,358 54,179 162,538 81,269 243,808 121,904 60,952 30,476 15,238 7,619 22,858 11,429 34,288 17,144 8,572 4,286 2,143 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

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