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Atlas › Integer Profiles › Node 27,686,144

27,686,144

28 × 83 × 1303
Abundant Even Composite

27,686,144 factors as 2^8 × 83 × 1303. Its 36 positive divisors give a proper-divisor sum of 28,286,752, so this integer is abundant. The Collatz stopping time is 74 steps.

Prime Factor Structure

Factorization String 2^8 × 83 × 1303
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 55,972,896
Proper Divisor Sum 28,286,752
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #27686129 ← → #27686179

Radix Representation

Decimal 27686144
Binary 1101001100111010100000000 (25 bits)
Octal 0o151472400
Hexadecimal 0x1A67500

Divisor Catalog (36)

1 2 4 8 16 32 64 83 128 166 256 332 664 1,303 1,328 2,606 2,656 5,212 5,312 10,424 10,624 20,848 21,248 41,696 83,392 108,149 166,784 216,298 333,568 432,596 865,192 1,730,384 3,460,768 6,921,536 13,843,072 27,686,144

Collatz Trajectory (74 steps to reach 1)

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

27,686,144 13,843,072 6,921,536 3,460,768 1,730,384 865,192 432,596 216,298 108,149 324,448 162,224 81,112 40,556 20,278 10,139 30,418 15,209 45,628 22,814 11,407 34,222 17,111 51,334 25,667 77,002 38,501 115,504 57,752 28,876 14,438 7,219 21,658 10,829 32,488 16,244 8,122 4,061 12,184 6,092 3,046 1,523 4,570 2,285 6,856 3,428 1,714 857 2,572 1,286 643 1,930 965 2,896 1,448 724 362 181 544 272 136

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