λ
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Atlas › Integer Profiles › Node 52,984,100

52,984,100

22 × 52 × 13 × 53 × 769
Abundant Even Composite

52,984,100 factors as 2^2 × 5^2 × 13 × 53 × 769. Its 72 positive divisors give a proper-divisor sum of 73,335,940, so this integer is abundant. The Collatz stopping time is 194 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 13 × 53 × 769
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 126,320,040
Proper Divisor Sum 73,335,940
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #52984093 ← → #52984117

Radix Representation

Decimal 52984100
Binary 11001010000111100100100100 (26 bits)
Octal 0o312074444
Hexadecimal 0x3287924

Divisor Catalog (60 of 72)

1 2 4 5 10 13 20 25 26 50 52 53 65 100 106 130 212 260 265 325 530 650 689 769 1,060 1,300 1,325 1,378 1,538 2,650 2,756 3,076 3,445 3,845 5,300 6,890 7,690 9,997 13,780 15,380 17,225 19,225 19,994 34,450 38,450 39,988 40,757 49,985 68,900 76,900 81,514 99,970 163,028 199,940 203,785 249,925 407,570 499,850 529,841 815,140

Collatz Trajectory (194 steps to reach 1)

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

52,984,100 26,492,050 13,246,025 39,738,076 19,869,038 9,934,519 29,803,558 14,901,779 44,705,338 22,352,669 67,058,008 33,529,004 16,764,502 8,382,251 25,146,754 12,573,377 37,720,132 18,860,066 9,430,033 28,290,100 14,145,050 7,072,525 21,217,576 10,608,788 5,304,394 2,652,197 7,956,592 3,978,296 1,989,148 994,574 497,287 1,491,862 745,931 2,237,794 1,118,897 3,356,692 1,678,346 839,173 2,517,520 1,258,760 629,380 314,690 157,345 472,036 236,018 118,009 354,028 177,014 88,507 265,522 132,761 398,284 199,142 99,571 298,714 149,357 448,072 224,036 112,018 56,009

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