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Atlas › Integer Profiles › Node 34,007,120

34,007,120

24 × 5 × 7 × 60727
Abundant Even Composite

34,007,120 factors as 2^4 × 5 × 7 × 60727. Its 40 positive divisors give a proper-divisor sum of 56,356,144, so this integer is abundant. The Collatz stopping time is 126 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 60727
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 90,363,264
Proper Divisor Sum 56,356,144
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #34007063 ← → #34007143

Radix Representation

Decimal 34007120
Binary 10000001101110100001010000 (26 bits)
Octal 0o201564120
Hexadecimal 0x206E850

Divisor Catalog (40)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 280 560 60,727 121,454 242,908 303,635 425,089 485,816 607,270 850,178 971,632 1,214,540 1,700,356 2,125,445 2,429,080 3,400,712 4,250,890 4,858,160 6,801,424 8,501,780 17,003,560 34,007,120

Collatz Trajectory (126 steps to reach 1)

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

34,007,120 17,003,560 8,501,780 4,250,890 2,125,445 6,376,336 3,188,168 1,594,084 797,042 398,521 1,195,564 597,782 298,891 896,674 448,337 1,345,012 672,506 336,253 1,008,760 504,380 252,190 126,095 378,286 189,143 567,430 283,715 851,146 425,573 1,276,720 638,360 319,180 159,590 79,795 239,386 119,693 359,080 179,540 89,770 44,885 134,656 67,328 33,664 16,832 8,416 4,208 2,104 1,052 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167

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