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Atlas › Integer Profiles › Node 2,211,040

2,211,040

25 × 5 × 13 × 1063
Abundant Even Composite

2,211,040 factors as 2^5 × 5 × 13 × 1063. Its 48 positive divisors give a proper-divisor sum of 3,419,648, so this integer is abundant. The Collatz stopping time is 73 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 13 × 1063
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 5,630,688
Proper Divisor Sum 3,419,648
Digit Sum / Digital Root 10 (Root: 1)
Adjacent Primes #2211029 ← → #2211061

Radix Representation

Decimal 2211040
Binary 1000011011110011100000 (22 bits)
Octal 0o10336340
Hexadecimal 0x21BCE0

Divisor Catalog (48)

1 2 4 5 8 10 13 16 20 26 32 40 52 65 80 104 130 160 208 260 416 520 1,040 1,063 2,080 2,126 4,252 5,315 8,504 10,630 13,819 17,008 21,260 27,638 34,016 42,520 55,276 69,095 85,040 110,552 138,190 170,080 221,104 276,380 442,208 552,760 1,105,520 2,211,040

Collatz Trajectory (73 steps to reach 1)

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

2,211,040 1,105,520 552,760 276,380 138,190 69,095 207,286 103,643 310,930 155,465 466,396 233,198 116,599 349,798 174,899 524,698 262,349 787,048 393,524 196,762 98,381 295,144 147,572 73,786 36,893 110,680 55,340 27,670 13,835 41,506 20,753 62,260 31,130 15,565 46,696 23,348 11,674 5,837 17,512 8,756 4,378 2,189 6,568 3,284 1,642 821 2,464 1,232 616 308 154 77 232 116 58 29 88 44 22 11

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