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Atlas › Integer Profiles › Node 7,579,005

7,579,005

3 × 5 × 7 × 19 × 29 × 131
Abundant Odd Composite

7,579,005 factors as 3 × 5 × 7 × 19 × 29 × 131. Its 64 positive divisors give a proper-divisor sum of 7,627,395, so this integer is abundant. The Collatz stopping time is 142 steps.

Prime Factor Structure

Factorization String 3 × 5 × 7 × 19 × 29 × 131
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 15,206,400
Proper Divisor Sum 7,627,395
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #7579003 ← → #7579027

Radix Representation

Decimal 7579005
Binary 11100111010010101111101 (23 bits)
Octal 0o34722575
Hexadecimal 0x73A57D

Divisor Catalog (60 of 64)

1 3 5 7 15 19 21 29 35 57 87 95 105 131 133 145 203 285 393 399 435 551 609 655 665 917 1,015 1,653 1,965 1,995 2,489 2,751 2,755 3,045 3,799 3,857 4,585 7,467 8,265 11,397 11,571 12,445 13,755 17,423 18,995 19,285 26,593 37,335 52,269 56,985 57,855 72,181 79,779 87,115 132,965 216,543 261,345 360,905 398,895 505,267

Collatz Trajectory (142 steps to reach 1)

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

7,579,005 22,737,016 11,368,508 5,684,254 2,842,127 8,526,382 4,263,191 12,789,574 6,394,787 19,184,362 9,592,181 28,776,544 14,388,272 7,194,136 3,597,068 1,798,534 899,267 2,697,802 1,348,901 4,046,704 2,023,352 1,011,676 505,838 252,919 758,758 379,379 1,138,138 569,069 1,707,208 853,604 426,802 213,401 640,204 320,102 160,051 480,154 240,077 720,232 360,116 180,058 90,029 270,088 135,044 67,522 33,761 101,284 50,642 25,321 75,964 37,982 18,991 56,974 28,487 85,462 42,731 128,194 64,097 192,292 96,146 48,073

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