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Atlas › Integer Profiles › Node 13,653,136

13,653,136

24 × 7 × 139 × 877
Abundant Even Composite

13,653,136 factors as 2^4 × 7 × 139 × 877. Its 40 positive divisors give a proper-divisor sum of 16,831,024, so this integer is abundant. The Collatz stopping time is 78 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 139 × 877
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 30,484,160
Proper Divisor Sum 16,831,024
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #13653127 ← → #13653137

Radix Representation

Decimal 13653136
Binary 110100000101010010010000 (24 bits)
Octal 0o64052220
Hexadecimal 0xD05490

Divisor Catalog (40)

1 2 4 7 8 14 16 28 56 112 139 278 556 877 973 1,112 1,754 1,946 2,224 3,508 3,892 6,139 7,016 7,784 12,278 14,032 15,568 24,556 49,112 98,224 121,903 243,806 487,612 853,321 975,224 1,706,642 1,950,448 3,413,284 6,826,568 13,653,136

Collatz Trajectory (78 steps to reach 1)

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

13,653,136 6,826,568 3,413,284 1,706,642 853,321 2,559,964 1,279,982 639,991 1,919,974 959,987 2,879,962 1,439,981 4,319,944 2,159,972 1,079,986 539,993 1,619,980 809,990 404,995 1,214,986 607,493 1,822,480 911,240 455,620 227,810 113,905 341,716 170,858 85,429 256,288 128,144 64,072 32,036 16,018 8,009 24,028 12,014 6,007 18,022 9,011 27,034 13,517 40,552 20,276 10,138 5,069 15,208 7,604 3,802 1,901 5,704 2,852 1,426 713 2,140 1,070 535 1,606 803 2,410

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