λ
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Atlas › Integer Profiles › Node 85,680,826

85,680,826

2 × 7 × 112 × 37 × 1367
Deficient Even Composite

85,680,826 factors as 2 × 7 × 11^2 × 37 × 1367. Its 48 positive divisors give a proper-divisor sum of 80,252,102, so this integer is deficient. The Collatz stopping time is 174 steps.

Prime Factor Structure

Factorization String 2 × 7 × 11^2 × 37 × 1367
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 165,932,928
Proper Divisor Sum 80,252,102
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #85680821 ← → #85680841

Radix Representation

Decimal 85680826
Binary 101000110110110001010111010 (27 bits)
Octal 0o506661272
Hexadecimal 0x51B62BA

Divisor Catalog (48)

1 2 7 11 14 22 37 74 77 121 154 242 259 407 518 814 847 1,367 1,694 2,734 2,849 4,477 5,698 8,954 9,569 15,037 19,138 30,074 31,339 50,579 62,678 101,158 105,259 165,407 210,518 330,814 354,053 556,369 708,106 1,112,738 1,157,849 2,315,698 3,894,583 6,120,059 7,789,166 12,240,118 42,840,413 85,680,826

Collatz Trajectory (174 steps to reach 1)

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

85,680,826 42,840,413 128,521,240 64,260,620 32,130,310 16,065,155 48,195,466 24,097,733 72,293,200 36,146,600 18,073,300 9,036,650 4,518,325 13,554,976 6,777,488 3,388,744 1,694,372 847,186 423,593 1,270,780 635,390 317,695 953,086 476,543 1,429,630 714,815 2,144,446 1,072,223 3,216,670 1,608,335 4,825,006 2,412,503 7,237,510 3,618,755 10,856,266 5,428,133 16,284,400 8,142,200 4,071,100 2,035,550 1,017,775 3,053,326 1,526,663 4,579,990 2,289,995 6,869,986 3,434,993 10,304,980 5,152,490 2,576,245 7,728,736 3,864,368 1,932,184 966,092 483,046 241,523 724,570 362,285 1,086,856 543,428

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