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Atlas › Integer Profiles › Node 19,088,000

19,088,000

27 × 53 × 1193
Abundant Even Composite

19,088,000 factors as 2^7 × 5^3 × 1193. Its 64 positive divisors give a proper-divisor sum of 28,409,320, so this integer is abundant. The Collatz stopping time is 102 steps.

Prime Factor Structure

Factorization String 2^7 × 5^3 × 1193
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 47,497,320
Proper Divisor Sum 28,409,320
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #19087997 ← → #19088011

Radix Representation

Decimal 19088000
Binary 1001000110100001010000000 (25 bits)
Octal 0o110641200
Hexadecimal 0x1234280

Divisor Catalog (60 of 64)

1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 125 128 160 200 250 320 400 500 640 800 1,000 1,193 1,600 2,000 2,386 3,200 4,000 4,772 5,965 8,000 9,544 11,930 16,000 19,088 23,860 29,825 38,176 47,720 59,650 76,352 95,440 119,300 149,125 152,704 190,880 238,600 298,250 381,760 477,200 596,500 763,520 954,400 1,193,000 1,908,800 2,386,000

Collatz Trajectory (102 steps to reach 1)

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

19,088,000 9,544,000 4,772,000 2,386,000 1,193,000 596,500 298,250 149,125 447,376 223,688 111,844 55,922 27,961 83,884 41,942 20,971 62,914 31,457 94,372 47,186 23,593 70,780 35,390 17,695 53,086 26,543 79,630 39,815 119,446 59,723 179,170 89,585 268,756 134,378 67,189 201,568 100,784 50,392 25,196 12,598 6,299 18,898 9,449 28,348 14,174 7,087 21,262 10,631 31,894 15,947 47,842 23,921 71,764 35,882 17,941 53,824 26,912 13,456 6,728 3,364

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