λ
Ratio Atlas
Atlas › Integer Profiles › Node 82,263,760

82,263,760

24 × 5 × 97 × 10601
Abundant Even Composite

82,263,760 factors as 2^4 × 5 × 97 × 10601. Its 40 positive divisors give a proper-divisor sum of 110,989,496, so this integer is abundant. The Collatz stopping time is 254 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 97 × 10601
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 193,253,256
Proper Divisor Sum 110,989,496
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #82263751 ← → #82263763

Radix Representation

Decimal 82263760
Binary 100111001110011111011010000 (27 bits)
Octal 0o471637320
Hexadecimal 0x4E73ED0

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 80 97 194 388 485 776 970 1,552 1,940 3,880 7,760 10,601 21,202 42,404 53,005 84,808 106,010 169,616 212,020 424,040 848,080 1,028,297 2,056,594 4,113,188 5,141,485 8,226,376 10,282,970 16,452,752 20,565,940 41,131,880 82,263,760

Collatz Trajectory (254 steps to reach 1)

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

82,263,760 41,131,880 20,565,940 10,282,970 5,141,485 15,424,456 7,712,228 3,856,114 1,928,057 5,784,172 2,892,086 1,446,043 4,338,130 2,169,065 6,507,196 3,253,598 1,626,799 4,880,398 2,440,199 7,320,598 3,660,299 10,980,898 5,490,449 16,471,348 8,235,674 4,117,837 12,353,512 6,176,756 3,088,378 1,544,189 4,632,568 2,316,284 1,158,142 579,071 1,737,214 868,607 2,605,822 1,302,911 3,908,734 1,954,367 5,863,102 2,931,551 8,794,654 4,397,327 13,191,982 6,595,991 19,787,974 9,893,987 29,681,962 14,840,981 44,522,944 22,261,472 11,130,736 5,565,368 2,782,684 1,391,342 695,671 2,087,014 1,043,507 3,130,522

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