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Atlas › Integer Profiles › Node 13,802,472

13,802,472

23 × 32 × 53 × 3617
Abundant Even Composite

13,802,472 factors as 2^3 × 3^2 × 53 × 3617. Its 48 positive divisors give a proper-divisor sum of 24,295,068, so this integer is abundant. The Collatz stopping time is 86 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 53 × 3617
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 38,097,540
Proper Divisor Sum 24,295,068
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #13802449 ← → #13802483

Radix Representation

Decimal 13802472
Binary 110100101001101111101000 (24 bits)
Octal 0o64515750
Hexadecimal 0xD29BE8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 53 72 106 159 212 318 424 477 636 954 1,272 1,908 3,617 3,816 7,234 10,851 14,468 21,702 28,936 32,553 43,404 65,106 86,808 130,212 191,701 260,424 383,402 575,103 766,804 1,150,206 1,533,608 1,725,309 2,300,412 3,450,618 4,600,824 6,901,236 13,802,472

Collatz Trajectory (86 steps to reach 1)

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

13,802,472 6,901,236 3,450,618 1,725,309 5,175,928 2,587,964 1,293,982 646,991 1,940,974 970,487 2,911,462 1,455,731 4,367,194 2,183,597 6,550,792 3,275,396 1,637,698 818,849 2,456,548 1,228,274 614,137 1,842,412 921,206 460,603 1,381,810 690,905 2,072,716 1,036,358 518,179 1,554,538 777,269 2,331,808 1,165,904 582,952 291,476 145,738 72,869 218,608 109,304 54,652 27,326 13,663 40,990 20,495 61,486 30,743 92,230 46,115 138,346 69,173 207,520 103,760 51,880 25,940 12,970 6,485 19,456 9,728 4,864 2,432

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