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Atlas › Integer Profiles › Node 47,736

47,736

23 × 33 × 13 × 17
Abundant Even Composite

Prime Factor Structure

Factorization String 2^3 × 3^3 × 13 × 17
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 151,200
Proper Divisor Sum 103,464
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #47717 ← → #47737

Radix Representation

Decimal 47736
Binary 1011101001111000 (16 bits)
Octal 0o135170
Hexadecimal 0xBA78

Divisor Catalog (60 of 64)

1 2 3 4 6 8 9 12 13 17 18 24 26 27 34 36 39 51 52 54 68 72 78 102 104 108 117 136 153 156 204 216 221 234 306 312 351 408 442 459 468 612 663 702 884 918 936 1,224 1,326 1,404 1,768 1,836 1,989 2,652 2,808 3,672 3,978 5,304 5,967 7,956

Collatz Trajectory (145 steps to reach 1)

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

47,736 23,868 11,934 5,967 17,902 8,951 26,854 13,427 40,282 20,141 60,424 30,212 15,106 7,553 22,660 11,330 5,665 16,996 8,498 4,249 12,748 6,374 3,187 9,562 4,781 14,344 7,172 3,586 1,793 5,380 2,690 1,345 4,036 2,018 1,009 3,028 1,514 757 2,272 1,136 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310

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