417,408

2⁷ × 3 × 1087

417,408 factors as 2^7 × 3 × 1087. Its 32 positive divisors give a proper-divisor sum of 692,352, so this integer is abundant. The Collatz stopping time is 143 steps.

Prime Factor Structure

Factorization String 2^7 × 3 × 1087

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,109,760

Proper Divisor Sum 692,352

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #417383 ← → #417419

Radix Representation

Decimal	417408
Binary	1100101111010000000 (19 bits)
Octal	0o1457200
Hexadecimal	0x65E80

Divisor Catalog (32)

1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 384 1,087 2,174 3,261 4,348 6,522 8,696 13,044 17,392 26,088 34,784 52,176 69,568 104,352 139,136 208,704 417,408

Collatz Trajectory (143 steps to reach 1)

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

417,408 208,704 104,352 52,176 26,088 13,044 6,522 3,261 9,784 4,892 2,446 1,223 3,670 1,835 5,506 2,753 8,260 4,130 2,065 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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