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Atlas › Integer Profiles › Node 71,821,456

71,821,456

24 × 73 × 23 × 569
Abundant Even Composite

71,821,456 factors as 2^4 × 7^3 × 23 × 569. Its 80 positive divisors give a proper-divisor sum of 97,810,544, so this integer is abundant. The Collatz stopping time is 114 steps.

Prime Factor Structure

Factorization String 2^4 × 7^3 × 23 × 569
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 169,632,000
Proper Divisor Sum 97,810,544
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #71821441 ← → #71821471

Radix Representation

Decimal 71821456
Binary 100010001111110100010010000 (27 bits)
Octal 0o421764220
Hexadecimal 0x447E890

Divisor Catalog (60 of 80)

1 2 4 7 8 14 16 23 28 46 49 56 92 98 112 161 184 196 322 343 368 392 569 644 686 784 1,127 1,138 1,288 1,372 2,254 2,276 2,576 2,744 3,983 4,508 4,552 5,488 7,889 7,966 9,016 9,104 13,087 15,778 15,932 18,032 26,174 27,881 31,556 31,864 52,348 55,762 63,112 63,728 91,609 104,696 111,524 126,224 183,218 195,167

Collatz Trajectory (114 steps to reach 1)

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

71,821,456 35,910,728 17,955,364 8,977,682 4,488,841 13,466,524 6,733,262 3,366,631 10,099,894 5,049,947 15,149,842 7,574,921 22,724,764 11,362,382 5,681,191 17,043,574 8,521,787 25,565,362 12,782,681 38,348,044 19,174,022 9,587,011 28,761,034 14,380,517 43,141,552 21,570,776 10,785,388 5,392,694 2,696,347 8,089,042 4,044,521 12,133,564 6,066,782 3,033,391 9,100,174 4,550,087 13,650,262 6,825,131 20,475,394 10,237,697 30,713,092 15,356,546 7,678,273 23,034,820 11,517,410 5,758,705 17,276,116 8,638,058 4,319,029 12,957,088 6,478,544 3,239,272 1,619,636 809,818 404,909 1,214,728 607,364 303,682 151,841 455,524

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