λ
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Atlas › Integer Profiles › Node 4,892,112

4,892,112

24 × 32 × 53 × 641
Abundant Even Composite

Starting at 4,892,112, the Collatz iteration reaches 1 after 113 steps. The first transition is 2446056; the starting value is even with 60 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 53 × 641
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 13,971,204
Proper Divisor Sum 9,079,092
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #4892099 ← → #4892149

Radix Representation

Decimal 4892112
Binary 10010101010010111010000 (23 bits)
Octal 0o22522720
Hexadecimal 0x4AA5D0

Divisor Catalog (60)

1 2 3 4 6 8 9 12 16 18 24 36 48 53 72 106 144 159 212 318 424 477 636 641 848 954 1,272 1,282 1,908 1,923 2,544 2,564 3,816 3,846 5,128 5,769 7,632 7,692 10,256 11,538 15,384 23,076 30,768 33,973 46,152 67,946 92,304 101,919 135,892 203,838 271,784 305,757 407,676 543,568 611,514 815,352 1,223,028 1,630,704 2,446,056 4,892,112

Collatz Trajectory (113 steps to reach 1)

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

4,892,112 2,446,056 1,223,028 611,514 305,757 917,272 458,636 229,318 114,659 343,978 171,989 515,968 257,984 128,992 64,496 32,248 16,124 8,062 4,031 12,094 6,047 18,142 9,071 27,214 13,607 40,822 20,411 61,234 30,617 91,852 45,926 22,963 68,890 34,445 103,336 51,668 25,834 12,917 38,752 19,376 9,688 4,844 2,422 1,211 3,634 1,817 5,452 2,726 1,363 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182

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