7,582,527

3² × 17 × 49559

Starting at 7,582,527, the Collatz iteration reaches 1 after 155 steps. The first transition is 22747582; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 17 × 49559

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 11,597,040

Proper Divisor Sum 4,014,513

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7582517 ← → #7582529

Radix Representation

Decimal	7582527
Binary	11100111011001100111111 (23 bits)
Octal	0o34731477
Hexadecimal	0x73B33F

Divisor Catalog (12)

1 3 9 17 51 153 49,559 148,677 446,031 842,503 2,527,509 7,582,527

Collatz Trajectory (155 steps to reach 1)

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

7,582,527 22,747,582 11,373,791 34,121,374 17,060,687 51,182,062 25,591,031 76,773,094 38,386,547 115,159,642 57,579,821 172,739,464 86,369,732 43,184,866 21,592,433 64,777,300 32,388,650 16,194,325 48,582,976 24,291,488 12,145,744 6,072,872 3,036,436 1,518,218 759,109 2,277,328 1,138,664 569,332 284,666 142,333 427,000 213,500 106,750 53,375 160,126 80,063 240,190 120,095 360,286 180,143 540,430 270,215 810,646 405,323 1,215,970 607,985 1,823,956 911,978 455,989 1,367,968 683,984 341,992 170,996 85,498 42,749 128,248 64,124 32,062 16,031 48,094

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