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Atlas › Integer Profiles › Node 20,731,648

20,731,648

28 × 7 × 23 × 503
Abundant Even Composite

20,731,648 factors as 2^8 × 7 × 23 × 503. Its 72 positive divisors give a proper-divisor sum of 28,716,800, so this integer is abundant. The Collatz stopping time is 84 steps.

Prime Factor Structure

Factorization String 2^8 × 7 × 23 × 503
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 49,448,448
Proper Divisor Sum 28,716,800
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #20731637 ← → #20731651

Radix Representation

Decimal 20731648
Binary 1001111000101011100000000 (25 bits)
Octal 0o117053400
Hexadecimal 0x13C5700

Divisor Catalog (60 of 72)

1 2 4 7 8 14 16 23 28 32 46 56 64 92 112 128 161 184 224 256 322 368 448 503 644 736 896 1,006 1,288 1,472 1,792 2,012 2,576 2,944 3,521 4,024 5,152 5,888 7,042 8,048 10,304 11,569 14,084 16,096 20,608 23,138 28,168 32,192 41,216 46,276 56,336 64,384 80,983 92,552 112,672 128,768 161,966 185,104 225,344 323,932

Collatz Trajectory (84 steps to reach 1)

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

20,731,648 10,365,824 5,182,912 2,591,456 1,295,728 647,864 323,932 161,966 80,983 242,950 121,475 364,426 182,213 546,640 273,320 136,660 68,330 34,165 102,496 51,248 25,624 12,812 6,406 3,203 9,610 4,805 14,416 7,208 3,604 1,802 901 2,704 1,352 676 338 169 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616

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