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Atlas › Integer Profiles › Node 13,613,664

13,613,664

25 × 3 × 109 × 1301
Abundant Even Composite

13,613,664 factors as 2^5 × 3 × 109 × 1301. Its 48 positive divisors give a proper-divisor sum of 22,477,776, so this integer is abundant. The Collatz stopping time is 86 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 109 × 1301
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 36,091,440
Proper Divisor Sum 22,477,776
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #13613657 ← → #13613687

Radix Representation

Decimal 13613664
Binary 110011111011101001100000 (24 bits)
Octal 0o63735140
Hexadecimal 0xCFBA60

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 48 96 109 218 327 436 654 872 1,301 1,308 1,744 2,602 2,616 3,488 3,903 5,204 5,232 7,806 10,408 10,464 15,612 20,816 31,224 41,632 62,448 124,896 141,809 283,618 425,427 567,236 850,854 1,134,472 1,701,708 2,268,944 3,403,416 4,537,888 6,806,832 13,613,664

Collatz Trajectory (86 steps to reach 1)

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

13,613,664 6,806,832 3,403,416 1,701,708 850,854 425,427 1,276,282 638,141 1,914,424 957,212 478,606 239,303 717,910 358,955 1,076,866 538,433 1,615,300 807,650 403,825 1,211,476 605,738 302,869 908,608 454,304 227,152 113,576 56,788 28,394 14,197 42,592 21,296 10,648 5,324 2,662 1,331 3,994 1,997 5,992 2,996 1,498 749 2,248 1,124 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404

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