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Atlas › Integer Profiles › Node 12,399,520

12,399,520

25 × 5 × 7 × 11071
Abundant Even Composite

12,399,520 factors as 2^5 × 5 × 7 × 11071. Its 48 positive divisors give a proper-divisor sum of 21,082,208, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 7 × 11071
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 33,481,728
Proper Divisor Sum 21,082,208
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #12399503 ← → #12399539

Radix Representation

Decimal 12399520
Binary 101111010011001110100000 (24 bits)
Octal 0o57231640
Hexadecimal 0xBD33A0

Divisor Catalog (48)

1 2 4 5 7 8 10 14 16 20 28 32 35 40 56 70 80 112 140 160 224 280 560 1,120 11,071 22,142 44,284 55,355 77,497 88,568 110,710 154,994 177,136 221,420 309,988 354,272 387,485 442,840 619,976 774,970 885,680 1,239,952 1,549,940 1,771,360 2,479,904 3,099,880 6,199,760 12,399,520

Collatz Trajectory (166 steps to reach 1)

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

12,399,520 6,199,760 3,099,880 1,549,940 774,970 387,485 1,162,456 581,228 290,614 145,307 435,922 217,961 653,884 326,942 163,471 490,414 245,207 735,622 367,811 1,103,434 551,717 1,655,152 827,576 413,788 206,894 103,447 310,342 155,171 465,514 232,757 698,272 349,136 174,568 87,284 43,642 21,821 65,464 32,732 16,366 8,183 24,550 12,275 36,826 18,413 55,240 27,620 13,810 6,905 20,716 10,358 5,179 15,538 7,769 23,308 11,654 5,827 17,482 8,741 26,224 13,112

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