417,672

2³ × 3² × 5801

417,672 has digital root 9. The neighboring primes are 417671 and 417691; its proper-divisor sum differs from the starting integer by 296,046.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 5801

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,131,390

Proper Divisor Sum 713,718

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #417671 ← → #417691

Radix Representation

Decimal	417672
Binary	1100101111110001000 (19 bits)
Octal	0o1457610
Hexadecimal	0x65F88

Divisor Catalog (24)

1 2 3 4 6 8 9 12 18 24 36 72 5,801 11,602 17,403 23,204 34,806 46,408 52,209 69,612 104,418 139,224 208,836 417,672

Collatz Trajectory (143 steps to reach 1)

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

417,672 208,836 104,418 52,209 156,628 78,314 39,157 117,472 58,736 29,368 14,684 7,342 3,671 11,014 5,507 16,522 8,261 24,784 12,392 6,196 3,098 1,549 4,648 2,324 1,162 581 1,744 872 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466

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