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Atlas › Integer Profiles › Node 6,836,616

6,836,616

23 × 33 × 31 × 1021
Abundant Even Composite

6,836,616 factors as 2^3 × 3^3 × 31 × 1021. Its 64 positive divisors give a proper-divisor sum of 12,785,784, so this integer is abundant. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 31 × 1021
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 19,622,400
Proper Divisor Sum 12,785,784
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #6836603 ← → #6836623

Radix Representation

Decimal 6836616
Binary 11010000101000110001000 (23 bits)
Octal 0o32050610
Hexadecimal 0x685188

Divisor Catalog (60 of 64)

1 2 3 4 6 8 9 12 18 24 27 31 36 54 62 72 93 108 124 186 216 248 279 372 558 744 837 1,021 1,116 1,674 2,042 2,232 3,063 3,348 4,084 6,126 6,696 8,168 9,189 12,252 18,378 24,504 27,567 31,651 36,756 55,134 63,302 73,512 94,953 110,268 126,604 189,906 220,536 253,208 284,859 379,812 569,718 759,624 854,577 1,139,436

Collatz Trajectory (134 steps to reach 1)

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

6,836,616 3,418,308 1,709,154 854,577 2,563,732 1,281,866 640,933 1,922,800 961,400 480,700 240,350 120,175 360,526 180,263 540,790 270,395 811,186 405,593 1,216,780 608,390 304,195 912,586 456,293 1,368,880 684,440 342,220 171,110 85,555 256,666 128,333 385,000 192,500 96,250 48,125 144,376 72,188 36,094 18,047 54,142 27,071 81,214 40,607 121,822 60,911 182,734 91,367 274,102 137,051 411,154 205,577 616,732 308,366 154,183 462,550 231,275 693,826 346,913 1,040,740 520,370 260,185

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