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Atlas › Integer Profiles › Node 20,184,736

20,184,736

25 × 112 × 13 × 401
Abundant Even Composite

20,184,736 factors as 2^5 × 11^2 × 13 × 401. Its 72 positive divisors give a proper-divisor sum of 26,972,276, so this integer is abundant. The Collatz stopping time is 133 steps.

Prime Factor Structure

Factorization String 2^5 × 11^2 × 13 × 401
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 47,157,012
Proper Divisor Sum 26,972,276
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #20184733 ← → #20184767

Radix Representation

Decimal 20184736
Binary 1001100111111111010100000 (25 bits)
Octal 0o114777240
Hexadecimal 0x133FEA0

Divisor Catalog (60 of 72)

1 2 4 8 11 13 16 22 26 32 44 52 88 104 121 143 176 208 242 286 352 401 416 484 572 802 968 1,144 1,573 1,604 1,936 2,288 3,146 3,208 3,872 4,411 4,576 5,213 6,292 6,416 8,822 10,426 12,584 12,832 17,644 20,852 25,168 35,288 41,704 48,521 50,336 57,343 70,576 83,408 97,042 114,686 141,152 166,816 194,084 229,372

Collatz Trajectory (133 steps to reach 1)

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

20,184,736 10,092,368 5,046,184 2,523,092 1,261,546 630,773 1,892,320 946,160 473,080 236,540 118,270 59,135 177,406 88,703 266,110 133,055 399,166 199,583 598,750 299,375 898,126 449,063 1,347,190 673,595 2,020,786 1,010,393 3,031,180 1,515,590 757,795 2,273,386 1,136,693 3,410,080 1,705,040 852,520 426,260 213,130 106,565 319,696 159,848 79,924 39,962 19,981 59,944 29,972 14,986 7,493 22,480 11,240 5,620 2,810 1,405 4,216 2,108 1,054 527 1,582 791 2,374 1,187 3,562

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