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Atlas › Integer Profiles › Node 19,972,160

19,972,160

26 × 5 × 13 × 4801
Abundant Even Composite

19,972,160 factors as 2^6 × 5 × 13 × 4801. Its 56 positive divisors give a proper-divisor sum of 31,255,576, so this integer is abundant. The Collatz stopping time is 283 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 13 × 4801
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 51,227,736
Proper Divisor Sum 31,255,576
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #19972157 ← → #19972181

Radix Representation

Decimal 19972160
Binary 1001100001100000001000000 (25 bits)
Octal 0o114140100
Hexadecimal 0x130C040

Divisor Catalog (56)

1 2 4 5 8 10 13 16 20 26 32 40 52 64 65 80 104 130 160 208 260 320 416 520 832 1,040 2,080 4,160 4,801 9,602 19,204 24,005 38,408 48,010 62,413 76,816 96,020 124,826 153,632 192,040 249,652 307,264 312,065 384,080 499,304 624,130 768,160 998,608 1,248,260 1,536,320 1,997,216 2,496,520 3,994,432 4,993,040 9,986,080 19,972,160

Collatz Trajectory (283 steps to reach 1)

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

19,972,160 9,986,080 4,993,040 2,496,520 1,248,260 624,130 312,065 936,196 468,098 234,049 702,148 351,074 175,537 526,612 263,306 131,653 394,960 197,480 98,740 49,370 24,685 74,056 37,028 18,514 9,257 27,772 13,886 6,943 20,830 10,415 31,246 15,623 46,870 23,435 70,306 35,153 105,460 52,730 26,365 79,096 39,548 19,774 9,887 29,662 14,831 44,494 22,247 66,742 33,371 100,114 50,057 150,172 75,086 37,543 112,630 56,315 168,946 84,473 253,420 126,710

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