λ
Ratio Atlas
Atlas › Integer Profiles › Node 1,100,008

1,100,008

23 × 7 × 13 × 1511
Abundant Even Composite

1,100,008 factors as 2^3 × 7 × 13 × 1511. Its 32 positive divisors give a proper-divisor sum of 1,440,152, so this integer is abundant. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 13 × 1511
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 2,540,160
Proper Divisor Sum 1,440,152
Digit Sum / Digital Root 10 (Root: 1)
Adjacent Primes #1099997 ← → #1100009

Radix Representation

Decimal 1100008
Binary 100001100100011101000 (21 bits)
Octal 0o4144350
Hexadecimal 0x10C8E8

Divisor Catalog (32)

1 2 4 7 8 13 14 26 28 52 56 91 104 182 364 728 1,511 3,022 6,044 10,577 12,088 19,643 21,154 39,286 42,308 78,572 84,616 137,501 157,144 275,002 550,004 1,100,008

Collatz Trajectory (134 steps to reach 1)

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

1,100,008 550,004 275,002 137,501 412,504 206,252 103,126 51,563 154,690 77,345 232,036 116,018 58,009 174,028 87,014 43,507 130,522 65,261 195,784 97,892 48,946 24,473 73,420 36,710 18,355 55,066 27,533 82,600 41,300 20,650 10,325 30,976 15,488 7,744 3,872 1,936 968 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186

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