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Atlas › Integer Profiles › Node 13,620,144

13,620,144

24 × 3 × 37 × 7669
Abundant Even Composite

13,620,144 factors as 2^4 × 3 × 37 × 7669. Its 40 positive divisors give a proper-divisor sum of 22,520,896, so this integer is abundant. The Collatz stopping time is 179 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 37 × 7669
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 36,141,040
Proper Divisor Sum 22,520,896
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #13620133 ← → #13620149

Radix Representation

Decimal 13620144
Binary 110011111101001110110000 (24 bits)
Octal 0o63751660
Hexadecimal 0xCFD3B0

Divisor Catalog (40)

1 2 3 4 6 8 12 16 24 37 48 74 111 148 222 296 444 592 888 1,776 7,669 15,338 23,007 30,676 46,014 61,352 92,028 122,704 184,056 283,753 368,112 567,506 851,259 1,135,012 1,702,518 2,270,024 3,405,036 4,540,048 6,810,072 13,620,144

Collatz Trajectory (179 steps to reach 1)

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

13,620,144 6,810,072 3,405,036 1,702,518 851,259 2,553,778 1,276,889 3,830,668 1,915,334 957,667 2,873,002 1,436,501 4,309,504 2,154,752 1,077,376 538,688 269,344 134,672 67,336 33,668 16,834 8,417 25,252 12,626 6,313 18,940 9,470 4,735 14,206 7,103 21,310 10,655 31,966 15,983 47,950 23,975 71,926 35,963 107,890 53,945 161,836 80,918 40,459 121,378 60,689 182,068 91,034 45,517 136,552 68,276 34,138 17,069 51,208 25,604 12,802 6,401 19,204 9,602 4,801 14,404

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