λ
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Atlas › Integer Profiles › Node 29,510,936

29,510,936

23 × 72 × 13 × 5791
Abundant Even Composite

29,510,936 factors as 2^3 × 7^2 × 13 × 5791. Its 48 positive divisors give a proper-divisor sum of 39,819,304, so this integer is abundant. The Collatz stopping time is 206 steps.

Prime Factor Structure

Factorization String 2^3 × 7^2 × 13 × 5791
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 69,330,240
Proper Divisor Sum 39,819,304
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #29510927 ← → #29510947

Radix Representation

Decimal 29510936
Binary 1110000100100110100011000 (25 bits)
Octal 0o160446430
Hexadecimal 0x1C24D18

Divisor Catalog (48)

1 2 4 7 8 13 14 26 28 49 52 56 91 98 104 182 196 364 392 637 728 1,274 2,548 5,096 5,791 11,582 23,164 40,537 46,328 75,283 81,074 150,566 162,148 283,759 301,132 324,296 526,981 567,518 602,264 1,053,962 1,135,036 2,107,924 2,270,072 3,688,867 4,215,848 7,377,734 14,755,468 29,510,936

Collatz Trajectory (206 steps to reach 1)

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

29,510,936 14,755,468 7,377,734 3,688,867 11,066,602 5,533,301 16,599,904 8,299,952 4,149,976 2,074,988 1,037,494 518,747 1,556,242 778,121 2,334,364 1,167,182 583,591 1,750,774 875,387 2,626,162 1,313,081 3,939,244 1,969,622 984,811 2,954,434 1,477,217 4,431,652 2,215,826 1,107,913 3,323,740 1,661,870 830,935 2,492,806 1,246,403 3,739,210 1,869,605 5,608,816 2,804,408 1,402,204 701,102 350,551 1,051,654 525,827 1,577,482 788,741 2,366,224 1,183,112 591,556 295,778 147,889 443,668 221,834 110,917 332,752 166,376 83,188 41,594 20,797 62,392 31,196

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