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Atlas › Integer Profiles › Node 34,401,752

34,401,752

23 × 7 × 112 × 5077
Abundant Even Composite

34,401,752 factors as 2^3 × 7 × 11^2 × 5077. Its 48 positive divisors give a proper-divisor sum of 46,643,128, so this integer is abundant. The Collatz stopping time is 201 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 11^2 × 5077
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 81,044,880
Proper Divisor Sum 46,643,128
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #34401737 ← → #34401781

Radix Representation

Decimal 34401752
Binary 10000011001110110111011000 (26 bits)
Octal 0o203166730
Hexadecimal 0x20CEDD8

Divisor Catalog (48)

1 2 4 7 8 11 14 22 28 44 56 77 88 121 154 242 308 484 616 847 968 1,694 3,388 5,077 6,776 10,154 20,308 35,539 40,616 55,847 71,078 111,694 142,156 223,388 284,312 390,929 446,776 614,317 781,858 1,228,634 1,563,716 2,457,268 3,127,432 4,300,219 4,914,536 8,600,438 17,200,876 34,401,752

Collatz Trajectory (201 steps to reach 1)

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

34,401,752 17,200,876 8,600,438 4,300,219 12,900,658 6,450,329 19,350,988 9,675,494 4,837,747 14,513,242 7,256,621 21,769,864 10,884,932 5,442,466 2,721,233 8,163,700 4,081,850 2,040,925 6,122,776 3,061,388 1,530,694 765,347 2,296,042 1,148,021 3,444,064 1,722,032 861,016 430,508 215,254 107,627 322,882 161,441 484,324 242,162 121,081 363,244 181,622 90,811 272,434 136,217 408,652 204,326 102,163 306,490 153,245 459,736 229,868 114,934 57,467 172,402 86,201 258,604 129,302 64,651 193,954 96,977 290,932 145,466 72,733 218,200

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