772,605

3³ × 5 × 59 × 97

772,605 has digital root 9. The neighboring primes are 772591 and 772619; its proper-divisor sum differs from the starting integer by -134,010.

Prime Factor Structure

Factorization String 3^3 × 5 × 59 × 97

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,411,200

Proper Divisor Sum 638,595

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #772591 ← → #772619

Radix Representation

Decimal	772605
Binary	10111100100111111101 (20 bits)
Octal	0o2744775
Hexadecimal	0xBC9FD

Divisor Catalog (32)

1 3 5 9 15 27 45 59 97 135 177 291 295 485 531 873 885 1,455 1,593 2,619 2,655 4,365 5,723 7,965 13,095 17,169 28,615 51,507 85,845 154,521 257,535 772,605

Collatz Trajectory (211 steps to reach 1)

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

772,605 2,317,816 1,158,908 579,454 289,727 869,182 434,591 1,303,774 651,887 1,955,662 977,831 2,933,494 1,466,747 4,400,242 2,200,121 6,600,364 3,300,182 1,650,091 4,950,274 2,475,137 7,425,412 3,712,706 1,856,353 5,569,060 2,784,530 1,392,265 4,176,796 2,088,398 1,044,199 3,132,598 1,566,299 4,698,898 2,349,449 7,048,348 3,524,174 1,762,087 5,286,262 2,643,131 7,929,394 3,964,697 11,894,092 5,947,046 2,973,523 8,920,570 4,460,285 13,380,856 6,690,428 3,345,214 1,672,607 5,017,822 2,508,911 7,526,734 3,763,367 11,290,102 5,645,051 16,935,154 8,467,577 25,402,732 12,701,366 6,350,683

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