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Atlas › Integer Profiles › Node 71,995,464

71,995,464

23 × 32 × 113 × 8849
Abundant Even Composite

71,995,464 factors as 2^3 × 3^2 × 113 × 8849. Its 48 positive divisors give a proper-divisor sum of 124,740,036, so this integer is abundant. The Collatz stopping time is 184 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 113 × 8849
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 196,735,500
Proper Divisor Sum 124,740,036
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #71995463 ← → #71995477

Radix Representation

Decimal 71995464
Binary 100010010101001000001001000 (27 bits)
Octal 0o422510110
Hexadecimal 0x44A9048

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 113 226 339 452 678 904 1,017 1,356 2,034 2,712 4,068 8,136 8,849 17,698 26,547 35,396 53,094 70,792 79,641 106,188 159,282 212,376 318,564 637,128 999,937 1,999,874 2,999,811 3,999,748 5,999,622 7,999,496 8,999,433 11,999,244 17,998,866 23,998,488 35,997,732 71,995,464

Collatz Trajectory (184 steps to reach 1)

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

71,995,464 35,997,732 17,998,866 8,999,433 26,998,300 13,499,150 6,749,575 20,248,726 10,124,363 30,373,090 15,186,545 45,559,636 22,779,818 11,389,909 34,169,728 17,084,864 8,542,432 4,271,216 2,135,608 1,067,804 533,902 266,951 800,854 400,427 1,201,282 600,641 1,801,924 900,962 450,481 1,351,444 675,722 337,861 1,013,584 506,792 253,396 126,698 63,349 190,048 95,024 47,512 23,756 11,878 5,939 17,818 8,909 26,728 13,364 6,682 3,341 10,024 5,012 2,506 1,253 3,760 1,880 940 470 235 706 353

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