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Atlas › Integer Profiles › Node 36,905,706

36,905,706

2 × 34 × 409 × 557
Abundant Even Composite

36,905,706 factors as 2 × 3^4 × 409 × 557. Its 40 positive divisors give a proper-divisor sum of 46,141,434, so this integer is abundant. The Collatz stopping time is 77 steps.

Prime Factor Structure

Factorization String 2 × 3^4 × 409 × 557
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 83,047,140
Proper Divisor Sum 46,141,434
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #36905689 ← → #36905741

Radix Representation

Decimal 36905706
Binary 10001100110010001011101010 (26 bits)
Octal 0o214621352
Hexadecimal 0x23322EA

Divisor Catalog (40)

1 2 3 6 9 18 27 54 81 162 409 557 818 1,114 1,227 1,671 2,454 3,342 3,681 5,013 7,362 10,026 11,043 15,039 22,086 30,078 33,129 45,117 66,258 90,234 227,813 455,626 683,439 1,366,878 2,050,317 4,100,634 6,150,951 12,301,902 18,452,853 36,905,706

Collatz Trajectory (77 steps to reach 1)

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

36,905,706 18,452,853 55,358,560 27,679,280 13,839,640 6,919,820 3,459,910 1,729,955 5,189,866 2,594,933 7,784,800 3,892,400 1,946,200 973,100 486,550 243,275 729,826 364,913 1,094,740 547,370 273,685 821,056 410,528 205,264 102,632 51,316 25,658 12,829 38,488 19,244 9,622 4,811 14,434 7,217 21,652 10,826 5,413 16,240 8,120 4,060 2,030 1,015 3,046 1,523 4,570 2,285 6,856 3,428 1,714 857 2,572 1,286 643 1,930 965 2,896 1,448 724 362 181

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