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Atlas › Integer Profiles › Node 7,052,584

7,052,584

23 × 7 × 11 × 1072
Abundant Even Composite

7,052,584 factors as 2^3 × 7 × 11 × 107^2. Its 48 positive divisors give a proper-divisor sum of 9,589,496, so this integer is abundant. The Collatz stopping time is 129 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 11 × 107^2
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 16,642,080
Proper Divisor Sum 9,589,496
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #7052581 ← → #7052599

Radix Representation

Decimal 7052584
Binary 11010111001110100101000 (23 bits)
Octal 0o32716450
Hexadecimal 0x6B9D28

Divisor Catalog (48)

1 2 4 7 8 11 14 22 28 44 56 77 88 107 154 214 308 428 616 749 856 1,177 1,498 2,354 2,996 4,708 5,992 8,239 9,416 11,449 16,478 22,898 32,956 45,796 65,912 80,143 91,592 125,939 160,286 251,878 320,572 503,756 641,144 881,573 1,007,512 1,763,146 3,526,292 7,052,584

Collatz Trajectory (129 steps to reach 1)

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

7,052,584 3,526,292 1,763,146 881,573 2,644,720 1,322,360 661,180 330,590 165,295 495,886 247,943 743,830 371,915 1,115,746 557,873 1,673,620 836,810 418,405 1,255,216 627,608 313,804 156,902 78,451 235,354 117,677 353,032 176,516 88,258 44,129 132,388 66,194 33,097 99,292 49,646 24,823 74,470 37,235 111,706 55,853 167,560 83,780 41,890 20,945 62,836 31,418 15,709 47,128 23,564 11,782 5,891 17,674 8,837 26,512 13,256 6,628 3,314 1,657 4,972 2,486 1,243

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