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Atlas › Integer Profiles › Node 86,123,772

86,123,772

22 × 32 × 72 × 48823
Abundant Even Composite

86,123,772 factors as 2^2 × 3^2 × 7^2 × 48823. Its 54 positive divisors give a proper-divisor sum of 167,126,316, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 7^2 × 48823
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 54
Divisor Sum (σ) 253,250,088
Proper Divisor Sum 167,126,316
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #86123729 ← → #86123773

Radix Representation

Decimal 86123772
Binary 101001000100010010011111100 (27 bits)
Octal 0o510422374
Hexadecimal 0x52224FC

Divisor Catalog (54)

1 2 3 4 6 7 9 12 14 18 21 28 36 42 49 63 84 98 126 147 196 252 294 441 588 882 1,764 48,823 97,646 146,469 195,292 292,938 341,761 439,407 585,876 683,522 878,814 1,025,283 1,367,044 1,757,628 2,050,566 2,392,327 3,075,849 4,101,132 4,784,654 6,151,698 7,176,981 9,569,308 12,303,396 14,353,962 21,530,943 28,707,924 43,061,886 86,123,772

Collatz Trajectory (192 steps to reach 1)

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

86,123,772 43,061,886 21,530,943 64,592,830 32,296,415 96,889,246 48,444,623 145,333,870 72,666,935 218,000,806 109,000,403 327,001,210 163,500,605 490,501,816 245,250,908 122,625,454 61,312,727 183,938,182 91,969,091 275,907,274 137,953,637 413,860,912 206,930,456 103,465,228 51,732,614 25,866,307 77,598,922 38,799,461 116,398,384 58,199,192 29,099,596 14,549,798 7,274,899 21,824,698 10,912,349 32,737,048 16,368,524 8,184,262 4,092,131 12,276,394 6,138,197 18,414,592 9,207,296 4,603,648 2,301,824 1,150,912 575,456 287,728 143,864 71,932 35,966 17,983 53,950 26,975 80,926 40,463 121,390 60,695 182,086 91,043

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