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Atlas › Integer Profiles › Node 6,728,256

6,728,256

26 × 32 × 11681
Abundant Even Composite

6,728,256 factors as 2^6 × 3^2 × 11681. Its 42 positive divisors give a proper-divisor sum of 12,558,726, so this integer is abundant. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 11681
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 42
Divisor Sum (σ) 19,286,982
Proper Divisor Sum 12,558,726
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #6728251 ← → #6728257

Radix Representation

Decimal 6728256
Binary 11001101010101001000000 (23 bits)
Octal 0o31525100
Hexadecimal 0x66AA40

Divisor Catalog (42)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 144 192 288 576 11,681 23,362 35,043 46,724 70,086 93,448 105,129 140,172 186,896 210,258 280,344 373,792 420,516 560,688 747,584 841,032 1,121,376 1,682,064 2,242,752 3,364,128 6,728,256

Collatz Trajectory (134 steps to reach 1)

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

6,728,256 3,364,128 1,682,064 841,032 420,516 210,258 105,129 315,388 157,694 78,847 236,542 118,271 354,814 177,407 532,222 266,111 798,334 399,167 1,197,502 598,751 1,796,254 898,127 2,694,382 1,347,191 4,041,574 2,020,787 6,062,362 3,031,181 9,093,544 4,546,772 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

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