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Atlas › Integer Profiles › Node 8,040,366

8,040,366

2 × 32 × 29 × 73 × 211
Abundant Even Composite

8,040,366 factors as 2 × 3^2 × 29 × 73 × 211. Its 48 positive divisors give a proper-divisor sum of 10,314,594, so this integer is abundant. The Collatz stopping time is 168 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 29 × 73 × 211
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 18,354,960
Proper Divisor Sum 10,314,594
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #8040341 ← → #8040367

Radix Representation

Decimal 8040366
Binary 11110101010111110101110 (23 bits)
Octal 0o36527656
Hexadecimal 0x7AAFAE

Divisor Catalog (48)

1 2 3 6 9 18 29 58 73 87 146 174 211 219 261 422 438 522 633 657 1,266 1,314 1,899 2,117 3,798 4,234 6,119 6,351 12,238 12,702 15,403 18,357 19,053 30,806 36,714 38,106 46,209 55,071 92,418 110,142 138,627 277,254 446,687 893,374 1,340,061 2,680,122 4,020,183 8,040,366

Collatz Trajectory (168 steps to reach 1)

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

8,040,366 4,020,183 12,060,550 6,030,275 18,090,826 9,045,413 27,136,240 13,568,120 6,784,060 3,392,030 1,696,015 5,088,046 2,544,023 7,632,070 3,816,035 11,448,106 5,724,053 17,172,160 8,586,080 4,293,040 2,146,520 1,073,260 536,630 268,315 804,946 402,473 1,207,420 603,710 301,855 905,566 452,783 1,358,350 679,175 2,037,526 1,018,763 3,056,290 1,528,145 4,584,436 2,292,218 1,146,109 3,438,328 1,719,164 859,582 429,791 1,289,374 644,687 1,934,062 967,031 2,901,094 1,450,547 4,351,642 2,175,821 6,527,464 3,263,732 1,631,866 815,933 2,447,800 1,223,900 611,950 305,975

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