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Atlas › Integer Profiles › Node 31,106,946

31,106,946

2 × 3 × 13 × 41 × 71 × 137
Abundant Even Composite

31,106,946 factors as 2 × 3 × 13 × 41 × 71 × 137. Its 64 positive divisors give a proper-divisor sum of 39,001,470, so this integer is abundant. The Collatz stopping time is 281 steps.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 41 × 71 × 137
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 70,108,416
Proper Divisor Sum 39,001,470
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #31106941 ← → #31106947

Radix Representation

Decimal 31106946
Binary 1110110101010011110000010 (25 bits)
Octal 0o166523602
Hexadecimal 0x1DAA782

Divisor Catalog (60 of 64)

1 2 3 6 13 26 39 41 71 78 82 123 137 142 213 246 274 411 426 533 822 923 1,066 1,599 1,781 1,846 2,769 2,911 3,198 3,562 5,343 5,538 5,617 5,822 8,733 9,727 10,686 11,234 16,851 17,466 19,454 29,181 33,702 37,843 58,362 73,021 75,686 113,529 126,451 146,042 219,063 227,058 252,902 379,353 398,807 438,126 758,706 797,614 1,196,421 2,392,842

Collatz Trajectory (281 steps to reach 1)

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

31,106,946 15,553,473 46,660,420 23,330,210 11,665,105 34,995,316 17,497,658 8,748,829 26,246,488 13,123,244 6,561,622 3,280,811 9,842,434 4,921,217 14,763,652 7,381,826 3,690,913 11,072,740 5,536,370 2,768,185 8,304,556 4,152,278 2,076,139 6,228,418 3,114,209 9,342,628 4,671,314 2,335,657 7,006,972 3,503,486 1,751,743 5,255,230 2,627,615 7,882,846 3,941,423 11,824,270 5,912,135 17,736,406 8,868,203 26,604,610 13,302,305 39,906,916 19,953,458 9,976,729 29,930,188 14,965,094 7,482,547 22,447,642 11,223,821 33,671,464 16,835,732 8,417,866 4,208,933 12,626,800 6,313,400 3,156,700 1,578,350 789,175 2,367,526 1,183,763

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