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Atlas › Integer Profiles › Node 8,239,509

8,239,509

33 × 17 × 29 × 619
Deficient Odd Composite

8,239,509 factors as 3^3 × 17 × 29 × 619. Its 32 positive divisors give a proper-divisor sum of 5,152,491, so this integer is deficient. The Collatz stopping time is 155 steps.

Prime Factor Structure

Factorization String 3^3 × 17 × 29 × 619
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 13,392,000
Proper Divisor Sum 5,152,491
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8239501 ← → #8239513

Radix Representation

Decimal 8239509
Binary 11111011011100110010101 (23 bits)
Octal 0o37334625
Hexadecimal 0x7DB995

Divisor Catalog (32)

1 3 9 17 27 29 51 87 153 261 459 493 619 783 1,479 1,857 4,437 5,571 10,523 13,311 16,713 17,951 31,569 53,853 94,707 161,559 284,121 305,167 484,677 915,501 2,746,503 8,239,509

Collatz Trajectory (155 steps to reach 1)

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

8,239,509 24,718,528 12,359,264 6,179,632 3,089,816 1,544,908 772,454 386,227 1,158,682 579,341 1,738,024 869,012 434,506 217,253 651,760 325,880 162,940 81,470 40,735 122,206 61,103 183,310 91,655 274,966 137,483 412,450 206,225 618,676 309,338 154,669 464,008 232,004 116,002 58,001 174,004 87,002 43,501 130,504 65,252 32,626 16,313 48,940 24,470 12,235 36,706 18,353 55,060 27,530 13,765 41,296 20,648 10,324 5,162 2,581 7,744 3,872 1,936 968 484 242

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