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Atlas › Integer Profiles › Node 12,377,841

12,377,841

3 × 73 × 23 × 523
Deficient Odd Composite

12,377,841 factors as 3 × 7^3 × 23 × 523. Its 32 positive divisors give a proper-divisor sum of 7,743,759, so this integer is deficient. The Collatz stopping time is 104 steps.

Prime Factor Structure

Factorization String 3 × 7^3 × 23 × 523
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 20,121,600
Proper Divisor Sum 7,743,759
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #12377791 ← → #12377843

Radix Representation

Decimal 12377841
Binary 101111001101111011110001 (24 bits)
Octal 0o57157361
Hexadecimal 0xBCDEF1

Divisor Catalog (32)

1 3 7 21 23 49 69 147 161 343 483 523 1,029 1,127 1,569 3,381 3,661 7,889 10,983 12,029 23,667 25,627 36,087 76,881 84,203 179,389 252,609 538,167 589,421 1,768,263 4,125,947 12,377,841

Collatz Trajectory (104 steps to reach 1)

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

12,377,841 37,133,524 18,566,762 9,283,381 27,850,144 13,925,072 6,962,536 3,481,268 1,740,634 870,317 2,610,952 1,305,476 652,738 326,369 979,108 489,554 244,777 734,332 367,166 183,583 550,750 275,375 826,126 413,063 1,239,190 619,595 1,858,786 929,393 2,788,180 1,394,090 697,045 2,091,136 1,045,568 522,784 261,392 130,696 65,348 32,674 16,337 49,012 24,506 12,253 36,760 18,380 9,190 4,595 13,786 6,893 20,680 10,340 5,170 2,585 7,756 3,878 1,939 5,818 2,909 8,728 4,364 2,182

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