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Atlas › Integer Profiles › Node 19,982,000

19,982,000

24 × 53 × 97 × 103
Abundant Even Composite

19,982,000 factors as 2^4 × 5^3 × 97 × 103. Its 80 positive divisors give a proper-divisor sum of 29,306,512, so this integer is abundant. The Collatz stopping time is 164 steps.

Prime Factor Structure

Factorization String 2^4 × 5^3 × 97 × 103
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 49,288,512
Proper Divisor Sum 29,306,512
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #19981999 ← → #19982029

Radix Representation

Decimal 19982000
Binary 1001100001110011010110000 (25 bits)
Octal 0o114163260
Hexadecimal 0x130E6B0

Divisor Catalog (60 of 80)

1 2 4 5 8 10 16 20 25 40 50 80 97 100 103 125 194 200 206 250 388 400 412 485 500 515 776 824 970 1,000 1,030 1,552 1,648 1,940 2,000 2,060 2,425 2,575 3,880 4,120 4,850 5,150 7,760 8,240 9,700 9,991 10,300 12,125 12,875 19,400 19,982 20,600 24,250 25,750 38,800 39,964 41,200 48,500 49,955 51,500

Collatz Trajectory (164 steps to reach 1)

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

19,982,000 9,991,000 4,995,500 2,497,750 1,248,875 3,746,626 1,873,313 5,619,940 2,809,970 1,404,985 4,214,956 2,107,478 1,053,739 3,161,218 1,580,609 4,741,828 2,370,914 1,185,457 3,556,372 1,778,186 889,093 2,667,280 1,333,640 666,820 333,410 166,705 500,116 250,058 125,029 375,088 187,544 93,772 46,886 23,443 70,330 35,165 105,496 52,748 26,374 13,187 39,562 19,781 59,344 29,672 14,836 7,418 3,709 11,128 5,564 2,782 1,391 4,174 2,087 6,262 3,131 9,394 4,697 14,092 7,046 3,523

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