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Atlas › Integer Profiles › Node 85,520,144

85,520,144

24 × 509 × 10501
Deficient Even Composite

85,520,144 factors as 2^4 × 509 × 10501. Its 20 positive divisors give a proper-divisor sum of 80,516,476, so this integer is deficient. The Collatz stopping time is 148 steps.

Prime Factor Structure

Factorization String 2^4 × 509 × 10501
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 166,036,620
Proper Divisor Sum 80,516,476
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #85520143 ← → #85520173

Radix Representation

Decimal 85520144
Binary 101000110001110111100010000 (27 bits)
Octal 0o506167420
Hexadecimal 0x518EF10

Divisor Catalog (20)

1 2 4 8 16 509 1,018 2,036 4,072 8,144 10,501 21,002 42,004 84,008 168,016 5,345,009 10,690,018 21,380,036 42,760,072 85,520,144

Collatz Trajectory (148 steps to reach 1)

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

85,520,144 42,760,072 21,380,036 10,690,018 5,345,009 16,035,028 8,017,514 4,008,757 12,026,272 6,013,136 3,006,568 1,503,284 751,642 375,821 1,127,464 563,732 281,866 140,933 422,800 211,400 105,700 52,850 26,425 79,276 39,638 19,819 59,458 29,729 89,188 44,594 22,297 66,892 33,446 16,723 50,170 25,085 75,256 37,628 18,814 9,407 28,222 14,111 42,334 21,167 63,502 31,751 95,254 47,627 142,882 71,441 214,324 107,162 53,581 160,744 80,372 40,186 20,093 60,280 30,140 15,070

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