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Atlas › Integer Profiles › Node 83,508,568

83,508,568

23 × 11 × 13 × 72997
Abundant Even Composite

83,508,568 factors as 2^3 × 11 × 13 × 72997. Its 32 positive divisors give a proper-divisor sum of 100,446,392, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2^3 × 11 × 13 × 72997
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 183,954,960
Proper Divisor Sum 100,446,392
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #83508547 ← → #83508571

Radix Representation

Decimal 83508568
Binary 100111110100011110101011000 (27 bits)
Octal 0o476436530
Hexadecimal 0x4FA3D58

Divisor Catalog (32)

1 2 4 8 11 13 22 26 44 52 88 104 143 286 572 1,144 72,997 145,994 291,988 583,976 802,967 948,961 1,605,934 1,897,922 3,211,868 3,795,844 6,423,736 7,591,688 10,438,571 20,877,142 41,754,284 83,508,568

Collatz Trajectory (99 steps to reach 1)

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

83,508,568 41,754,284 20,877,142 10,438,571 31,315,714 15,657,857 46,973,572 23,486,786 11,743,393 35,230,180 17,615,090 8,807,545 26,422,636 13,211,318 6,605,659 19,816,978 9,908,489 29,725,468 14,862,734 7,431,367 22,294,102 11,147,051 33,441,154 16,720,577 50,161,732 25,080,866 12,540,433 37,621,300 18,810,650 9,405,325 28,215,976 14,107,988 7,053,994 3,526,997 10,580,992 5,290,496 2,645,248 1,322,624 661,312 330,656 165,328 82,664 41,332 20,666 10,333 31,000 15,500 7,750 3,875 11,626 5,813 17,440 8,720 4,360 2,180 1,090 545 1,636 818 409

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