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Atlas › Integer Profiles › Node 1,688,160

1,688,160

25 × 3 × 5 × 3517
Abundant Even Composite

1,688,160 factors as 2^5 × 3 × 5 × 3517. Its 48 positive divisors give a proper-divisor sum of 3,631,056, so this integer is abundant. The Collatz stopping time is 83 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 3517
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 5,319,216
Proper Divisor Sum 3,631,056
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #1688153 ← → #1688161

Radix Representation

Decimal 1688160
Binary 110011100001001100000 (21 bits)
Octal 0o6341140
Hexadecimal 0x19C260

Divisor Catalog (48)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 80 96 120 160 240 480 3,517 7,034 10,551 14,068 17,585 21,102 28,136 35,170 42,204 52,755 56,272 70,340 84,408 105,510 112,544 140,680 168,816 211,020 281,360 337,632 422,040 562,720 844,080 1,688,160

Collatz Trajectory (83 steps to reach 1)

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

1,688,160 844,080 422,040 211,020 105,510 52,755 158,266 79,133 237,400 118,700 59,350 29,675 89,026 44,513 133,540 66,770 33,385 100,156 50,078 25,039 75,118 37,559 112,678 56,339 169,018 84,509 253,528 126,764 63,382 31,691 95,074 47,537 142,612 71,306 35,653 106,960 53,480 26,740 13,370 6,685 20,056 10,028 5,014 2,507 7,522 3,761 11,284 5,642 2,821 8,464 4,232 2,116 1,058 529 1,588 794 397 1,192 596 298

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