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Atlas › Integer Profiles › Node 1,667,568

1,667,568

24 × 3 × 72 × 709
Abundant Even Composite

1,667,568 factors as 2^4 × 3 × 7^2 × 709. Its 60 positive divisors give a proper-divisor sum of 3,350,712, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 7^2 × 709
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 5,018,280
Proper Divisor Sum 3,350,712
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #1667551 ← → #1667579

Radix Representation

Decimal 1667568
Binary 110010111000111110000 (21 bits)
Octal 0o6270760
Hexadecimal 0x1971F0

Divisor Catalog (60)

1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 49 56 84 98 112 147 168 196 294 336 392 588 709 784 1,176 1,418 2,127 2,352 2,836 4,254 4,963 5,672 8,508 9,926 11,344 14,889 17,016 19,852 29,778 34,032 34,741 39,704 59,556 69,482 79,408 104,223 119,112 138,964 208,446 238,224 277,928 416,892 555,856 833,784 1,667,568

Collatz Trajectory (176 steps to reach 1)

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

1,667,568 833,784 416,892 208,446 104,223 312,670 156,335 469,006 234,503 703,510 351,755 1,055,266 527,633 1,582,900 791,450 395,725 1,187,176 593,588 296,794 148,397 445,192 222,596 111,298 55,649 166,948 83,474 41,737 125,212 62,606 31,303 93,910 46,955 140,866 70,433 211,300 105,650 52,825 158,476 79,238 39,619 118,858 59,429 178,288 89,144 44,572 22,286 11,143 33,430 16,715 50,146 25,073 75,220 37,610 18,805 56,416 28,208 14,104 7,052 3,526 1,763

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