λ
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Atlas › Integer Profiles › Node 8,022,012

8,022,012

22 × 3 × 167 × 4003
Abundant Even Composite

8,022,012 factors as 2^2 × 3 × 167 × 4003. Its 24 positive divisors give a proper-divisor sum of 10,812,804, so this integer is abundant. The Collatz stopping time is 230 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 167 × 4003
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 18,834,816
Proper Divisor Sum 10,812,804
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #8021999 ← → #8022017

Radix Representation

Decimal 8022012
Binary 11110100110011111111100 (23 bits)
Octal 0o36463774
Hexadecimal 0x7A67FC

Divisor Catalog (24)

1 2 3 4 6 12 167 334 501 668 1,002 2,004 4,003 8,006 12,009 16,012 24,018 48,036 668,501 1,337,002 2,005,503 2,674,004 4,011,006 8,022,012

Collatz Trajectory (230 steps to reach 1)

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

8,022,012 4,011,006 2,005,503 6,016,510 3,008,255 9,024,766 4,512,383 13,537,150 6,768,575 20,305,726 10,152,863 30,458,590 15,229,295 45,687,886 22,843,943 68,531,830 34,265,915 102,797,746 51,398,873 154,196,620 77,098,310 38,549,155 115,647,466 57,823,733 173,471,200 86,735,600 43,367,800 21,683,900 10,841,950 5,420,975 16,262,926 8,131,463 24,394,390 12,197,195 36,591,586 18,295,793 54,887,380 27,443,690 13,721,845 41,165,536 20,582,768 10,291,384 5,145,692 2,572,846 1,286,423 3,859,270 1,929,635 5,788,906 2,894,453 8,683,360 4,341,680 2,170,840 1,085,420 542,710 271,355 814,066 407,033 1,221,100 610,550 305,275

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