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Atlas › Integer Profiles › Node 2,188,104

2,188,104

23 × 3 × 17 × 31 × 173
Abundant Even Composite

2,188,104 factors as 2^3 × 3 × 17 × 31 × 173. Its 64 positive divisors give a proper-divisor sum of 3,825,336, so this integer is abundant. The Collatz stopping time is 171 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 17 × 31 × 173
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 6,013,440
Proper Divisor Sum 3,825,336
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #2188099 ← → #2188111

Radix Representation

Decimal 2188104
Binary 1000010110001101001000 (22 bits)
Octal 0o10261510
Hexadecimal 0x216348

Divisor Catalog (60 of 64)

1 2 3 4 6 8 12 17 24 31 34 51 62 68 93 102 124 136 173 186 204 248 346 372 408 519 527 692 744 1,038 1,054 1,384 1,581 2,076 2,108 2,941 3,162 4,152 4,216 5,363 5,882 6,324 8,823 10,726 11,764 12,648 16,089 17,646 21,452 23,528 32,178 35,292 42,904 64,356 70,584 91,171 128,712 182,342 273,513 364,684

Collatz Trajectory (171 steps to reach 1)

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

2,188,104 1,094,052 547,026 273,513 820,540 410,270 205,135 615,406 307,703 923,110 461,555 1,384,666 692,333 2,077,000 1,038,500 519,250 259,625 778,876 389,438 194,719 584,158 292,079 876,238 438,119 1,314,358 657,179 1,971,538 985,769 2,957,308 1,478,654 739,327 2,217,982 1,108,991 3,326,974 1,663,487 4,990,462 2,495,231 7,485,694 3,742,847 11,228,542 5,614,271 16,842,814 8,421,407 25,264,222 12,632,111 37,896,334 18,948,167 56,844,502 28,422,251 85,266,754 42,633,377 127,900,132 63,950,066 31,975,033 95,925,100 47,962,550 23,981,275 71,943,826 35,971,913 107,915,740

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