83,000,664

2³ × 3² × 17 × 19 × 43 × 83

83,000,664 factors as 2^3 × 3^2 × 17 × 19 × 43 × 83. Its 192 positive divisors give a proper-divisor sum of 176,458,536, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 17 × 19 × 43 × 83

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 192

Divisor Sum (σ) 259,459,200

Proper Divisor Sum 176,458,536

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #83000663 ← → #83000699

Radix Representation

Decimal	83000664
Binary	100111100100111110101011000 (27 bits)
Octal	0o474476530
Hexadecimal	0x4F27D58

Divisor Catalog (60 of 192)

1 2 3 4 6 8 9 12 17 18 19 24 34 36 38 43 51 57 68 72 76 83 86 102 114 129 136 152 153 166 171 172 204 228 249 258 306 323 332 342 344 387 408 456 498 516 612 646 664 684 731 747 774 817 969 996 1,032 1,224 1,292 1,368

Collatz Trajectory (192 steps to reach 1)

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

83,000,664 41,500,332 20,750,166 10,375,083 31,125,250 15,562,625 46,687,876 23,343,938 11,671,969 35,015,908 17,507,954 8,753,977 26,261,932 13,130,966 6,565,483 19,696,450 9,848,225 29,544,676 14,772,338 7,386,169 22,158,508 11,079,254 5,539,627 16,618,882 8,309,441 24,928,324 12,464,162 6,232,081 18,696,244 9,348,122 4,674,061 14,022,184 7,011,092 3,505,546 1,752,773 5,258,320 2,629,160 1,314,580 657,290 328,645 985,936 492,968 246,484 123,242 61,621 184,864 92,432 46,216 23,108 11,554 5,777 17,332 8,666 4,333 13,000 6,500 3,250 1,625 4,876 2,438

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