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Atlas › Integer Profiles › Node 83,382,016

83,382,016

28 × 37 × 8803
Abundant Even Composite

83,382,016 factors as 2^8 × 37 × 8803. Its 36 positive divisors give a proper-divisor sum of 87,574,056, so this integer is abundant. The Collatz stopping time is 205 steps.

Prime Factor Structure

Factorization String 2^8 × 37 × 8803
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 170,956,072
Proper Divisor Sum 87,574,056
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #83382001 ← → #83382017

Radix Representation

Decimal 83382016
Binary 100111110000100111100000000 (27 bits)
Octal 0o476047400
Hexadecimal 0x4F84F00

Divisor Catalog (36)

1 2 4 8 16 32 37 64 74 128 148 256 296 592 1,184 2,368 4,736 8,803 9,472 17,606 35,212 70,424 140,848 281,696 325,711 563,392 651,422 1,126,784 1,302,844 2,253,568 2,605,688 5,211,376 10,422,752 20,845,504 41,691,008 83,382,016

Collatz Trajectory (205 steps to reach 1)

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

83,382,016 41,691,008 20,845,504 10,422,752 5,211,376 2,605,688 1,302,844 651,422 325,711 977,134 488,567 1,465,702 732,851 2,198,554 1,099,277 3,297,832 1,648,916 824,458 412,229 1,236,688 618,344 309,172 154,586 77,293 231,880 115,940 57,970 28,985 86,956 43,478 21,739 65,218 32,609 97,828 48,914 24,457 73,372 36,686 18,343 55,030 27,515 82,546 41,273 123,820 61,910 30,955 92,866 46,433 139,300 69,650 34,825 104,476 52,238 26,119 78,358 39,179 117,538 58,769 176,308 88,154

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