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Atlas › Integer Profiles › Node 84,317,320

84,317,320

23 × 5 × 41 × 51413
Abundant Even Composite

84,317,320 factors as 2^3 × 5 × 41 × 51413. Its 32 positive divisors give a proper-divisor sum of 110,027,600, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 41 × 51413
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 194,344,920
Proper Divisor Sum 110,027,600
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #84317309 ← → #84317351

Radix Representation

Decimal 84317320
Binary 101000001101001010010001000 (27 bits)
Octal 0o501512210
Hexadecimal 0x5069488

Divisor Catalog (32)

1 2 4 5 8 10 20 40 41 82 164 205 328 410 820 1,640 51,413 102,826 205,652 257,065 411,304 514,130 1,028,260 2,056,520 2,107,933 4,215,866 8,431,732 10,539,665 16,863,464 21,079,330 42,158,660 84,317,320

Collatz Trajectory (192 steps to reach 1)

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

84,317,320 42,158,660 21,079,330 10,539,665 31,618,996 15,809,498 7,904,749 23,714,248 11,857,124 5,928,562 2,964,281 8,892,844 4,446,422 2,223,211 6,669,634 3,334,817 10,004,452 5,002,226 2,501,113 7,503,340 3,751,670 1,875,835 5,627,506 2,813,753 8,441,260 4,220,630 2,110,315 6,330,946 3,165,473 9,496,420 4,748,210 2,374,105 7,122,316 3,561,158 1,780,579 5,341,738 2,670,869 8,012,608 4,006,304 2,003,152 1,001,576 500,788 250,394 125,197 375,592 187,796 93,898 46,949 140,848 70,424 35,212 17,606 8,803 26,410 13,205 39,616 19,808 9,904 4,952 2,476

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