λ
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Atlas › Integer Profiles › Node 7,020,006

7,020,006

2 × 3 × 7 × 192 × 463
Abundant Even Composite

7,020,006 factors as 2 × 3 × 7 × 19^2 × 463. Its 48 positive divisors give a proper-divisor sum of 9,951,258, so this integer is abundant. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 19^2 × 463
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 16,971,264
Proper Divisor Sum 9,951,258
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #7019993 ← → #7020023

Radix Representation

Decimal 7020006
Binary 11010110001110111100110 (23 bits)
Octal 0o32616746
Hexadecimal 0x6B1DE6

Divisor Catalog (48)

1 2 3 6 7 14 19 21 38 42 57 114 133 266 361 399 463 722 798 926 1,083 1,389 2,166 2,527 2,778 3,241 5,054 6,482 7,581 8,797 9,723 15,162 17,594 19,446 26,391 52,782 61,579 123,158 167,143 184,737 334,286 369,474 501,429 1,002,858 1,170,001 2,340,002 3,510,003 7,020,006

Collatz Trajectory (178 steps to reach 1)

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

7,020,006 3,510,003 10,530,010 5,265,005 15,795,016 7,897,508 3,948,754 1,974,377 5,923,132 2,961,566 1,480,783 4,442,350 2,221,175 6,663,526 3,331,763 9,995,290 4,997,645 14,992,936 7,496,468 3,748,234 1,874,117 5,622,352 2,811,176 1,405,588 702,794 351,397 1,054,192 527,096 263,548 131,774 65,887 197,662 98,831 296,494 148,247 444,742 222,371 667,114 333,557 1,000,672 500,336 250,168 125,084 62,542 31,271 93,814 46,907 140,722 70,361 211,084 105,542 52,771 158,314 79,157 237,472 118,736 59,368 29,684 14,842 7,421

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