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Atlas › Integer Profiles › Node 2,199,768

2,199,768

23 × 3 × 151 × 607
Abundant Even Composite

2,199,768 factors as 2^3 × 3 × 151 × 607. Its 32 positive divisors give a proper-divisor sum of 3,345,192, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 151 × 607
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 5,544,960
Proper Divisor Sum 3,345,192
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #2199739 ← → #2199781

Radix Representation

Decimal 2199768
Binary 1000011001000011011000 (22 bits)
Octal 0o10310330
Hexadecimal 0x2190D8

Divisor Catalog (32)

1 2 3 4 6 8 12 24 151 302 453 604 607 906 1,208 1,214 1,812 1,821 2,428 3,624 3,642 4,856 7,284 14,568 91,657 183,314 274,971 366,628 549,942 733,256 1,099,884 2,199,768

Collatz Trajectory (91 steps to reach 1)

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

2,199,768 1,099,884 549,942 274,971 824,914 412,457 1,237,372 618,686 309,343 928,030 464,015 1,392,046 696,023 2,088,070 1,044,035 3,132,106 1,566,053 4,698,160 2,349,080 1,174,540 587,270 293,635 880,906 440,453 1,321,360 660,680 330,340 165,170 82,585 247,756 123,878 61,939 185,818 92,909 278,728 139,364 69,682 34,841 104,524 52,262 26,131 78,394 39,197 117,592 58,796 29,398 14,699 44,098 22,049 66,148 33,074 16,537 49,612 24,806 12,403 37,210 18,605 55,816 27,908 13,954

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