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Atlas › Integer Profiles › Node 13,837,120

13,837,120

26 × 5 × 11 × 3931
Abundant Even Composite

13,837,120 factors as 2^6 × 5 × 11 × 3931. Its 56 positive divisors give a proper-divisor sum of 22,117,088, so this integer is abundant. The Collatz stopping time is 47 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 11 × 3931
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 35,954,208
Proper Divisor Sum 22,117,088
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #13837079 ← → #13837121

Radix Representation

Decimal 13837120
Binary 110100110010001101000000 (24 bits)
Octal 0o64621500
Hexadecimal 0xD32340

Divisor Catalog (56)

1 2 4 5 8 10 11 16 20 22 32 40 44 55 64 80 88 110 160 176 220 320 352 440 704 880 1,760 3,520 3,931 7,862 15,724 19,655 31,448 39,310 43,241 62,896 78,620 86,482 125,792 157,240 172,964 216,205 251,584 314,480 345,928 432,410 628,960 691,856 864,820 1,257,920 1,383,712 1,729,640 2,767,424 3,459,280 6,918,560 13,837,120

Collatz Trajectory (47 steps to reach 1)

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

13,837,120 6,918,560 3,459,280 1,729,640 864,820 432,410 216,205 648,616 324,308 162,154 81,077 243,232 121,616 60,808 30,404 15,202 7,601 22,804 11,402 5,701 17,104 8,552 4,276 2,138 1,069 3,208 1,604 802 401 1,204 602 301 904 452 226 113 340 170 85 256 128 64 32 16 8 4 2 1

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