395,560

2³ × 5 × 11 × 29 × 31

395,560 factors as 2^3 × 5 × 11 × 29 × 31. Its 64 positive divisors give a proper-divisor sum of 641,240, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 11 × 29 × 31

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,036,800

Proper Divisor Sum 641,240

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #395543 ← → #395581

Radix Representation

Decimal	395560
Binary	1100000100100101000 (19 bits)
Octal	0o1404450
Hexadecimal	0x60928

Divisor Catalog (60 of 64)

1 2 4 5 8 10 11 20 22 29 31 40 44 55 58 62 88 110 116 124 145 155 220 232 248 290 310 319 341 440 580 620 638 682 899 1,160 1,240 1,276 1,364 1,595 1,705 1,798 2,552 2,728 3,190 3,410 3,596 4,495 6,380 6,820 7,192 8,990 9,889 12,760 13,640 17,980 19,778 35,960 39,556 49,445

Collatz Trajectory (99 steps to reach 1)

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

395,560 197,780 98,890 49,445 148,336 74,168 37,084 18,542 9,271 27,814 13,907 41,722 20,861 62,584 31,292 15,646 7,823 23,470 11,735 35,206 17,603 52,810 26,405 79,216 39,608 19,804 9,902 4,951 14,854 7,427 22,282 11,141 33,424 16,712 8,356 4,178 2,089 6,268 3,134 1,567 4,702 2,351 7,054 3,527 10,582 5,291 15,874 7,937 23,812 11,906 5,953 17,860 8,930 4,465 13,396 6,698 3,349 10,048 5,024 2,512

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