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Atlas › Integer Profiles › Node 8,167,116

8,167,116

22 × 3 × 23 × 127 × 233
Abundant Even Composite

8,167,116 factors as 2^2 × 3 × 23 × 127 × 233. Its 48 positive divisors give a proper-divisor sum of 11,960,628, so this integer is abundant. The Collatz stopping time is 155 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 23 × 127 × 233
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 20,127,744
Proper Divisor Sum 11,960,628
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #8167111 ← → #8167147

Radix Representation

Decimal 8167116
Binary 11111001001111011001100 (23 bits)
Octal 0o37117314
Hexadecimal 0x7C9ECC

Divisor Catalog (48)

1 2 3 4 6 12 23 46 69 92 127 138 233 254 276 381 466 508 699 762 932 1,398 1,524 2,796 2,921 5,359 5,842 8,763 10,718 11,684 16,077 17,526 21,436 29,591 32,154 35,052 59,182 64,308 88,773 118,364 177,546 355,092 680,593 1,361,186 2,041,779 2,722,372 4,083,558 8,167,116

Collatz Trajectory (155 steps to reach 1)

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

8,167,116 4,083,558 2,041,779 6,125,338 3,062,669 9,188,008 4,594,004 2,297,002 1,148,501 3,445,504 1,722,752 861,376 430,688 215,344 107,672 53,836 26,918 13,459 40,378 20,189 60,568 30,284 15,142 7,571 22,714 11,357 34,072 17,036 8,518 4,259 12,778 6,389 19,168 9,584 4,792 2,396 1,198 599 1,798 899 2,698 1,349 4,048 2,024 1,012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1,456

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