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Atlas › Integer Profiles › Node 36,388,120

36,388,120

23 × 5 × 163 × 5581
Abundant Even Composite

36,388,120 factors as 2^3 × 5 × 163 × 5581. Its 32 positive divisors give a proper-divisor sum of 46,002,200, so this integer is abundant. The Collatz stopping time is 108 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 163 × 5581
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 82,390,320
Proper Divisor Sum 46,002,200
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #36388063 ← → #36388129

Radix Representation

Decimal 36388120
Binary 10001010110011110100011000 (26 bits)
Octal 0o212636430
Hexadecimal 0x22B3D18

Divisor Catalog (32)

1 2 4 5 8 10 20 40 163 326 652 815 1,304 1,630 3,260 5,581 6,520 11,162 22,324 27,905 44,648 55,810 111,620 223,240 909,703 1,819,406 3,638,812 4,548,515 7,277,624 9,097,030 18,194,060 36,388,120

Collatz Trajectory (108 steps to reach 1)

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

36,388,120 18,194,060 9,097,030 4,548,515 13,645,546 6,822,773 20,468,320 10,234,160 5,117,080 2,558,540 1,279,270 639,635 1,918,906 959,453 2,878,360 1,439,180 719,590 359,795 1,079,386 539,693 1,619,080 809,540 404,770 202,385 607,156 303,578 151,789 455,368 227,684 113,842 56,921 170,764 85,382 42,691 128,074 64,037 192,112 96,056 48,028 24,014 12,007 36,022 18,011 54,034 27,017 81,052 40,526 20,263 60,790 30,395 91,186 45,593 136,780 68,390 34,195 102,586 51,293 153,880 76,940 38,470

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