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Atlas › Integer Profiles › Node 13,088,608

13,088,608

25 × 13 × 73 × 431
Abundant Even Composite

13,088,608 factors as 2^5 × 13 × 73 × 431. Its 48 positive divisors give a proper-divisor sum of 15,107,168, so this integer is abundant. The Collatz stopping time is 148 steps.

Prime Factor Structure

Factorization String 2^5 × 13 × 73 × 431
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 28,195,776
Proper Divisor Sum 15,107,168
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #13088591 ← → #13088627

Radix Representation

Decimal 13088608
Binary 110001111011011101100000 (24 bits)
Octal 0o61733540
Hexadecimal 0xC7B760

Divisor Catalog (48)

1 2 4 8 13 16 26 32 52 73 104 146 208 292 416 431 584 862 949 1,168 1,724 1,898 2,336 3,448 3,796 5,603 6,896 7,592 11,206 13,792 15,184 22,412 30,368 31,463 44,824 62,926 89,648 125,852 179,296 251,704 409,019 503,408 818,038 1,006,816 1,636,076 3,272,152 6,544,304 13,088,608

Collatz Trajectory (148 steps to reach 1)

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

13,088,608 6,544,304 3,272,152 1,636,076 818,038 409,019 1,227,058 613,529 1,840,588 920,294 460,147 1,380,442 690,221 2,070,664 1,035,332 517,666 258,833 776,500 388,250 194,125 582,376 291,188 145,594 72,797 218,392 109,196 54,598 27,299 81,898 40,949 122,848 61,424 30,712 15,356 7,678 3,839 11,518 5,759 17,278 8,639 25,918 12,959 38,878 19,439 58,318 29,159 87,478 43,739 131,218 65,609 196,828 98,414 49,207 147,622 73,811 221,434 110,717 332,152 166,076 83,038

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