λ
Ratio Atlas
Atlas › Integer Profiles › Node 408,384

408,384

26 × 32 × 709
Abundant Even Composite

408,384 factors as 2^6 × 3^2 × 709. Its 42 positive divisors give a proper-divisor sum of 763,826, so this integer is abundant. The Collatz stopping time is 81 steps.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 709
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 42
Divisor Sum (σ) 1,172,210
Proper Divisor Sum 763,826
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #408379 ← → #408389

Radix Representation

Decimal 408384
Binary 1100011101101000000 (19 bits)
Octal 0o1435500
Hexadecimal 0x63B40

Divisor Catalog (42)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 144 192 288 576 709 1,418 2,127 2,836 4,254 5,672 6,381 8,508 11,344 12,762 17,016 22,688 25,524 34,032 45,376 51,048 68,064 102,096 136,128 204,192 408,384

Collatz Trajectory (81 steps to reach 1)

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

408,384 204,192 102,096 51,048 25,524 12,762 6,381 19,144 9,572 4,786 2,393 7,180 3,590 1,795 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569 1,708 854 427 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86 43 130 65 196 98 49 148 74

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #408,383 Browse Full Index Next Integer #408,385 →