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Atlas › Integer Profiles › Node 19,472,000

19,472,000

27 × 53 × 1217
Abundant Even Composite

19,472,000 factors as 2^7 × 5^3 × 1217. Its 64 positive divisors give a proper-divisor sum of 28,980,040, so this integer is abundant. The Collatz stopping time is 71 steps.

Prime Factor Structure

Factorization String 2^7 × 5^3 × 1217
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 48,452,040
Proper Divisor Sum 28,980,040
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #19471997 ← → #19472003

Radix Representation

Decimal 19472000
Binary 1001010010001111010000000 (25 bits)
Octal 0o112217200
Hexadecimal 0x1291E80

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 1,217 1,600 2,000 2,434 3,200 4,000 4,868 6,085 8,000 9,736 12,170 16,000 19,472 24,340 30,425 38,944 48,680 60,850 77,888 97,360 121,700 152,125 155,776 194,720 243,400 304,250 389,440 486,800 608,500 778,880 973,600 1,217,000 1,947,200 2,434,000

Collatz Trajectory (71 steps to reach 1)

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

19,472,000 9,736,000 4,868,000 2,434,000 1,217,000 608,500 304,250 152,125 456,376 228,188 114,094 57,047 171,142 85,571 256,714 128,357 385,072 192,536 96,268 48,134 24,067 72,202 36,101 108,304 54,152 27,076 13,538 6,769 20,308 10,154 5,077 15,232 7,616 3,808 1,904 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17

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