λ
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Atlas › Integer Profiles › Node 51,605,092

51,605,092

22 × 7 × 11 × 131 × 1279
Abundant Even Composite

51,605,092 factors as 2^2 × 7 × 11 × 131 × 1279. Its 48 positive divisors give a proper-divisor sum of 61,936,028, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 11 × 131 × 1279
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 113,541,120
Proper Divisor Sum 61,936,028
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #51605063 ← → #51605131

Radix Representation

Decimal 51605092
Binary 11000100110110111001100100 (26 bits)
Octal 0o304667144
Hexadecimal 0x3136E64

Divisor Catalog (48)

1 2 4 7 11 14 22 28 44 77 131 154 262 308 524 917 1,279 1,441 1,834 2,558 2,882 3,668 5,116 5,764 8,953 10,087 14,069 17,906 20,174 28,138 35,812 40,348 56,276 98,483 167,549 196,966 335,098 393,932 670,196 1,172,843 1,843,039 2,345,686 3,686,078 4,691,372 7,372,156 12,901,273 25,802,546 51,605,092

Collatz Trajectory (137 steps to reach 1)

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

51,605,092 25,802,546 12,901,273 38,703,820 19,351,910 9,675,955 29,027,866 14,513,933 43,541,800 21,770,900 10,885,450 5,442,725 16,328,176 8,164,088 4,082,044 2,041,022 1,020,511 3,061,534 1,530,767 4,592,302 2,296,151 6,888,454 3,444,227 10,332,682 5,166,341 15,499,024 7,749,512 3,874,756 1,937,378 968,689 2,906,068 1,453,034 726,517 2,179,552 1,089,776 544,888 272,444 136,222 68,111 204,334 102,167 306,502 153,251 459,754 229,877 689,632 344,816 172,408 86,204 43,102 21,551 64,654 32,327 96,982 48,491 145,474 72,737 218,212 109,106 54,553

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