3,927,680

2⁷ × 5 × 17 × 19²

3,927,680 factors as 2^7 × 5 × 17 × 19^2. Its 96 positive divisors give a proper-divisor sum of 6,565,060, so this integer is abundant. The Collatz stopping time is 141 steps.

Prime Factor Structure

Factorization String 2^7 × 5 × 17 × 19^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 10,492,740

Proper Divisor Sum 6,565,060

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #3927667 ← → #3927691

Radix Representation

Decimal	3927680
Binary	1110111110111010000000 (22 bits)
Octal	0o16767200
Hexadecimal	0x3BEE80

Divisor Catalog (60 of 96)

1 2 4 5 8 10 16 17 19 20 32 34 38 40 64 68 76 80 85 95 128 136 152 160 170 190 272 304 320 323 340 361 380 544 608 640 646 680 722 760 1,088 1,216 1,292 1,360 1,444 1,520 1,615 1,805 2,176 2,432 2,584 2,720 2,888 3,040 3,230 3,610 5,168 5,440 5,776 6,080

Collatz Trajectory (141 steps to reach 1)

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

3,927,680 1,963,840 981,920 490,960 245,480 122,740 61,370 30,685 92,056 46,028 23,014 11,507 34,522 17,261 51,784 25,892 12,946 6,473 19,420 9,710 4,855 14,566 7,283 21,850 10,925 32,776 16,388 8,194 4,097 12,292 6,146 3,073 9,220 4,610 2,305 6,916 3,458 1,729 5,188 2,594 1,297 3,892 1,946 973 2,920 1,460 730 365 1,096 548 274 137 412 206 103 310 155 466 233 700

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