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Atlas › Integer Profiles › Node 6,579,006

6,579,006

2 × 3 × 7 × 312 × 163
Abundant Even Composite

6,579,006 factors as 2 × 3 × 7 × 31^2 × 163. Its 48 positive divisors give a proper-divisor sum of 9,054,786, so this integer is abundant. The Collatz stopping time is 90 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 31^2 × 163
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 15,633,792
Proper Divisor Sum 9,054,786
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #6578987 ← → #6579019

Radix Representation

Decimal 6579006
Binary 11001000110001100111110 (23 bits)
Octal 0o31061476
Hexadecimal 0x64633E

Divisor Catalog (48)

1 2 3 6 7 14 21 31 42 62 93 163 186 217 326 434 489 651 961 978 1,141 1,302 1,922 2,282 2,883 3,423 5,053 5,766 6,727 6,846 10,106 13,454 15,159 20,181 30,318 35,371 40,362 70,742 106,113 156,643 212,226 313,286 469,929 939,858 1,096,501 2,193,002 3,289,503 6,579,006

Collatz Trajectory (90 steps to reach 1)

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

6,579,006 3,289,503 9,868,510 4,934,255 14,802,766 7,401,383 22,204,150 11,102,075 33,306,226 16,653,113 49,959,340 24,979,670 12,489,835 37,469,506 18,734,753 56,204,260 28,102,130 14,051,065 42,153,196 21,076,598 10,538,299 31,614,898 15,807,449 47,422,348 23,711,174 11,855,587 35,566,762 17,783,381 53,350,144 26,675,072 13,337,536 6,668,768 3,334,384 1,667,192 833,596 416,798 208,399 625,198 312,599 937,798 468,899 1,406,698 703,349 2,110,048 1,055,024 527,512 263,756 131,878 65,939 197,818 98,909 296,728 148,364 74,182 37,091 111,274 55,637 166,912 83,456 41,728

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