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Atlas › Integer Profiles › Node 20,165,100

20,165,100

22 × 3 × 52 × 67217
Abundant Even Composite

20,165,100 factors as 2^2 × 3 × 5^2 × 67217. Its 36 positive divisors give a proper-divisor sum of 38,180,124, so this integer is abundant. The Collatz stopping time is 146 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^2 × 67217
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 58,345,224
Proper Divisor Sum 38,180,124
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #20165081 ← → #20165129

Radix Representation

Decimal 20165100
Binary 1001100111011000111101100 (25 bits)
Octal 0o114730754
Hexadecimal 0x133B1EC

Divisor Catalog (36)

1 2 3 4 5 6 10 12 15 20 25 30 50 60 75 100 150 300 67,217 134,434 201,651 268,868 336,085 403,302 672,170 806,604 1,008,255 1,344,340 1,680,425 2,016,510 3,360,850 4,033,020 5,041,275 6,721,700 10,082,550 20,165,100

Collatz Trajectory (146 steps to reach 1)

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

20,165,100 10,082,550 5,041,275 15,123,826 7,561,913 22,685,740 11,342,870 5,671,435 17,014,306 8,507,153 25,521,460 12,760,730 6,380,365 19,141,096 9,570,548 4,785,274 2,392,637 7,177,912 3,588,956 1,794,478 897,239 2,691,718 1,345,859 4,037,578 2,018,789 6,056,368 3,028,184 1,514,092 757,046 378,523 1,135,570 567,785 1,703,356 851,678 425,839 1,277,518 638,759 1,916,278 958,139 2,874,418 1,437,209 4,311,628 2,155,814 1,077,907 3,233,722 1,616,861 4,850,584 2,425,292 1,212,646 606,323 1,818,970 909,485 2,728,456 1,364,228 682,114 341,057 1,023,172 511,586 255,793 767,380

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