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93,480

23 × 3 × 5 × 19 × 41
Abundant Even Composite

93,480 factors as 2^3 × 3 × 5 × 19 × 41. Its 64 positive divisors give a proper-divisor sum of 208,920, so this integer is abundant. The Collatz stopping time is 84 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 19 × 41
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 302,400
Proper Divisor Sum 208,920
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #93479 ← → #93481

Radix Representation

Decimal 93480
Binary 10110110100101000 (17 bits)
Octal 0o266450
Hexadecimal 0x16D28

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 19 20 24 30 38 40 41 57 60 76 82 95 114 120 123 152 164 190 205 228 246 285 328 380 410 456 492 570 615 760 779 820 984 1,140 1,230 1,558 1,640 2,280 2,337 2,460 3,116 3,895 4,674 4,920 6,232 7,790 9,348 11,685 15,580 18,696

Collatz Trajectory (84 steps to reach 1)

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

93,480 46,740 23,370 11,685 35,056 17,528 8,764 4,382 2,191 6,574 3,287 9,862 4,931 14,794 7,397 22,192 11,096 5,548 2,774 1,387 4,162 2,081 6,244 3,122 1,561 4,684 2,342 1,171 3,514 1,757 5,272 2,636 1,318 659 1,978 989 2,968 1,484 742 371 1,114 557 1,672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101

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