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Atlas › Integer Profiles › Node 13,634,814

13,634,814

2 × 3 × 23 × 29 × 3407
Abundant Even Composite

13,634,814 factors as 2 × 3 × 23 × 29 × 3407. Its 32 positive divisors give a proper-divisor sum of 15,810,306, so this integer is abundant. The Collatz stopping time is 223 steps.

Prime Factor Structure

Factorization String 2 × 3 × 23 × 29 × 3407
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 29,445,120
Proper Divisor Sum 15,810,306
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #13634813 ← → #13634851

Radix Representation

Decimal 13634814
Binary 110100000000110011111110 (24 bits)
Octal 0o64006376
Hexadecimal 0xD00CFE

Divisor Catalog (32)

1 2 3 6 23 29 46 58 69 87 138 174 667 1,334 2,001 3,407 4,002 6,814 10,221 20,442 78,361 98,803 156,722 197,606 235,083 296,409 470,166 592,818 2,272,469 4,544,938 6,817,407 13,634,814

Collatz Trajectory (223 steps to reach 1)

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

13,634,814 6,817,407 20,452,222 10,226,111 30,678,334 15,339,167 46,017,502 23,008,751 69,026,254 34,513,127 103,539,382 51,769,691 155,309,074 77,654,537 232,963,612 116,481,806 58,240,903 174,722,710 87,361,355 262,084,066 131,042,033 393,126,100 196,563,050 98,281,525 294,844,576 147,422,288 73,711,144 36,855,572 18,427,786 9,213,893 27,641,680 13,820,840 6,910,420 3,455,210 1,727,605 5,182,816 2,591,408 1,295,704 647,852 323,926 161,963 485,890 242,945 728,836 364,418 182,209 546,628 273,314 136,657 409,972 204,986 102,493 307,480 153,740 76,870 38,435 115,306 57,653 172,960 86,480

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