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Atlas › Integer Profiles › Node 17,527,016

17,527,016

23 × 13 × 127 × 1327
Abundant Even Composite

17,527,016 factors as 2^3 × 13 × 127 × 1327. Its 32 positive divisors give a proper-divisor sum of 18,169,624, so this integer is abundant. The Collatz stopping time is 169 steps.

Prime Factor Structure

Factorization String 2^3 × 13 × 127 × 1327
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 35,696,640
Proper Divisor Sum 18,169,624
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #17527007 ← → #17527021

Radix Representation

Decimal 17527016
Binary 1000010110111000011101000 (25 bits)
Octal 0o102670350
Hexadecimal 0x10B70E8

Divisor Catalog (32)

1 2 4 8 13 26 52 104 127 254 508 1,016 1,327 1,651 2,654 3,302 5,308 6,604 10,616 13,208 17,251 34,502 69,004 138,008 168,529 337,058 674,116 1,348,232 2,190,877 4,381,754 8,763,508 17,527,016

Collatz Trajectory (169 steps to reach 1)

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

17,527,016 8,763,508 4,381,754 2,190,877 6,572,632 3,286,316 1,643,158 821,579 2,464,738 1,232,369 3,697,108 1,848,554 924,277 2,772,832 1,386,416 693,208 346,604 173,302 86,651 259,954 129,977 389,932 194,966 97,483 292,450 146,225 438,676 219,338 109,669 329,008 164,504 82,252 41,126 20,563 61,690 30,845 92,536 46,268 23,134 11,567 34,702 17,351 52,054 26,027 78,082 39,041 117,124 58,562 29,281 87,844 43,922 21,961 65,884 32,942 16,471 49,414 24,707 74,122 37,061 111,184

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