λ
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Atlas › Integer Profiles › Node 29,436,732

29,436,732

22 × 32 × 13 × 31 × 2029
Abundant Even Composite

29,436,732 factors as 2^2 × 3^2 × 13 × 31 × 2029. Its 72 positive divisors give a proper-divisor sum of 53,322,308, so this integer is abundant. The Collatz stopping time is 206 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 13 × 31 × 2029
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 82,759,040
Proper Divisor Sum 53,322,308
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #29436731 ← → #29436733

Radix Representation

Decimal 29436732
Binary 1110000010010101100111100 (25 bits)
Octal 0o160225474
Hexadecimal 0x1C12B3C

Divisor Catalog (60 of 72)

1 2 3 4 6 9 12 13 18 26 31 36 39 52 62 78 93 117 124 156 186 234 279 372 403 468 558 806 1,116 1,209 1,612 2,029 2,418 3,627 4,058 4,836 6,087 7,254 8,116 12,174 14,508 18,261 24,348 26,377 36,522 52,754 62,899 73,044 79,131 105,508 125,798 158,262 188,697 237,393 251,596 316,524 377,394 474,786 566,091 754,788

Collatz Trajectory (206 steps to reach 1)

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

29,436,732 14,718,366 7,359,183 22,077,550 11,038,775 33,116,326 16,558,163 49,674,490 24,837,245 74,511,736 37,255,868 18,627,934 9,313,967 27,941,902 13,970,951 41,912,854 20,956,427 62,869,282 31,434,641 94,303,924 47,151,962 23,575,981 70,727,944 35,363,972 17,681,986 8,840,993 26,522,980 13,261,490 6,630,745 19,892,236 9,946,118 4,973,059 14,919,178 7,459,589 22,378,768 11,189,384 5,594,692 2,797,346 1,398,673 4,196,020 2,098,010 1,049,005 3,147,016 1,573,508 786,754 393,377 1,180,132 590,066 295,033 885,100 442,550 221,275 663,826 331,913 995,740 497,870 248,935 746,806 373,403 1,120,210

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