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Atlas › Integer Profiles › Node 20,002,572

20,002,572

22 × 33 × 89 × 2081
Abundant Even Composite

20,002,572 factors as 2^2 × 3^3 × 89 × 2081. Its 48 positive divisors give a proper-divisor sum of 32,463,828, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 89 × 2081
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 52,466,400
Proper Divisor Sum 32,463,828
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #20002553 ← → #20002579

Radix Representation

Decimal 20002572
Binary 1001100010011011100001100 (25 bits)
Octal 0o114233414
Hexadecimal 0x131370C

Divisor Catalog (48)

1 2 3 4 6 9 12 18 27 36 54 89 108 178 267 356 534 801 1,068 1,602 2,081 2,403 3,204 4,162 4,806 6,243 8,324 9,612 12,486 18,729 24,972 37,458 56,187 74,916 112,374 185,209 224,748 370,418 555,627 740,836 1,111,254 1,666,881 2,222,508 3,333,762 5,000,643 6,667,524 10,001,286 20,002,572

Collatz Trajectory (138 steps to reach 1)

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

20,002,572 10,001,286 5,000,643 15,001,930 7,500,965 22,502,896 11,251,448 5,625,724 2,812,862 1,406,431 4,219,294 2,109,647 6,328,942 3,164,471 9,493,414 4,746,707 14,240,122 7,120,061 21,360,184 10,680,092 5,340,046 2,670,023 8,010,070 4,005,035 12,015,106 6,007,553 18,022,660 9,011,330 4,505,665 13,516,996 6,758,498 3,379,249 10,137,748 5,068,874 2,534,437 7,603,312 3,801,656 1,900,828 950,414 475,207 1,425,622 712,811 2,138,434 1,069,217 3,207,652 1,603,826 801,913 2,405,740 1,202,870 601,435 1,804,306 902,153 2,706,460 1,353,230 676,615 2,029,846 1,014,923 3,044,770 1,522,385 4,567,156

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