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Atlas › Integer Profiles › Node 3,978,288

3,978,288

24 × 33 × 9209
Abundant Even Composite

3,978,288 factors as 2^4 × 3^3 × 9209. Its 40 positive divisors give a proper-divisor sum of 7,442,112, so this integer is abundant. The Collatz stopping time is 141 steps.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 9209
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 11,420,400
Proper Divisor Sum 7,442,112
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #3978283 ← → #3978301

Radix Representation

Decimal 3978288
Binary 1111001011010000110000 (22 bits)
Octal 0o17132060
Hexadecimal 0x3CB430

Divisor Catalog (40)

1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 108 144 216 432 9,209 18,418 27,627 36,836 55,254 73,672 82,881 110,508 147,344 165,762 221,016 248,643 331,524 442,032 497,286 663,048 994,572 1,326,096 1,989,144 3,978,288

Collatz Trajectory (141 steps to reach 1)

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

3,978,288 1,989,144 994,572 497,286 248,643 745,930 372,965 1,118,896 559,448 279,724 139,862 69,931 209,794 104,897 314,692 157,346 78,673 236,020 118,010 59,005 177,016 88,508 44,254 22,127 66,382 33,191 99,574 49,787 149,362 74,681 224,044 112,022 56,011 168,034 84,017 252,052 126,026 63,013 189,040 94,520 47,260 23,630 11,815 35,446 17,723 53,170 26,585 79,756 39,878 19,939 59,818 29,909 89,728 44,864 22,432 11,216 5,608 2,804 1,402 701

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