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Atlas › Integer Profiles › Node 19,980,948

19,980,948

22 × 3 × 13 × 349 × 367
Abundant Even Composite

19,980,948 factors as 2^2 × 3 × 13 × 349 × 367. Its 48 positive divisors give a proper-divisor sum of 30,508,652, so this integer is abundant. The Collatz stopping time is 164 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 13 × 349 × 367
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 50,489,600
Proper Divisor Sum 30,508,652
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #19980943 ← → #19980959

Radix Representation

Decimal 19980948
Binary 1001100001110001010010100 (25 bits)
Octal 0o114161224
Hexadecimal 0x130E294

Divisor Catalog (48)

1 2 3 4 6 12 13 26 39 52 78 156 349 367 698 734 1,047 1,101 1,396 1,468 2,094 2,202 4,188 4,404 4,537 4,771 9,074 9,542 13,611 14,313 18,148 19,084 27,222 28,626 54,444 57,252 128,083 256,166 384,249 512,332 768,498 1,536,996 1,665,079 3,330,158 4,995,237 6,660,316 9,990,474 19,980,948

Collatz Trajectory (164 steps to reach 1)

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

19,980,948 9,990,474 4,995,237 14,985,712 7,492,856 3,746,428 1,873,214 936,607 2,809,822 1,404,911 4,214,734 2,107,367 6,322,102 3,161,051 9,483,154 4,741,577 14,224,732 7,112,366 3,556,183 10,668,550 5,334,275 16,002,826 8,001,413 24,004,240 12,002,120 6,001,060 3,000,530 1,500,265 4,500,796 2,250,398 1,125,199 3,375,598 1,687,799 5,063,398 2,531,699 7,595,098 3,797,549 11,392,648 5,696,324 2,848,162 1,424,081 4,272,244 2,136,122 1,068,061 3,204,184 1,602,092 801,046 400,523 1,201,570 600,785 1,802,356 901,178 450,589 1,351,768 675,884 337,942 168,971 506,914 253,457 760,372

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