311,984

2⁴ × 17 × 31 × 37

311,984 has digital root 8. The neighboring primes are 311981 and 312007; its proper-divisor sum differs from the starting integer by 54,560.

Prime Factor Structure

Factorization String 2^4 × 17 × 31 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 678,528

Proper Divisor Sum 366,544

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #311981 ← → #312007

Radix Representation

Decimal	311984
Binary	1001100001010110000 (19 bits)
Octal	0o1141260
Hexadecimal	0x4C2B0

Divisor Catalog (40)

1 2 4 8 16 17 31 34 37 62 68 74 124 136 148 248 272 296 496 527 592 629 1,054 1,147 1,258 2,108 2,294 2,516 4,216 4,588 5,032 8,432 9,176 10,064 18,352 19,499 38,998 77,996 155,992 311,984

Collatz Trajectory (52 steps to reach 1)

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

311,984 155,992 77,996 38,998 19,499 58,498 29,249 87,748 43,874 21,937 65,812 32,906 16,453 49,360 24,680 12,340 6,170 3,085 9,256 4,628 2,314 1,157 3,472 1,736 868 434 217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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