λ
Harmonic Matrix

709,677

32 × 78853
Deficient Odd Composite

709,677 has digital root 9. The neighboring primes are 709673 and 709679; its proper-divisor sum differs from the starting integer by -394,252.

Prime Factor Structure

Factorization String 3^2 × 78853
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 6
Divisor Sum (σ) 1,025,102
Proper Divisor Sum 315,425
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #709673 ← → #709679

Radix Representation

Decimal 709677
Binary 10101101010000101101 (20 bits)
Octal 0o2552055
Hexadecimal 0xAD42D

Divisor Catalog (6)

1 3 9 78,853 236,559 709,677

Collatz Trajectory (211 steps to reach 1)

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

709,677 2,129,032 1,064,516 532,258 266,129 798,388 399,194 199,597 598,792 299,396 149,698 74,849 224,548 112,274 56,137 168,412 84,206 42,103 126,310 63,155 189,466 94,733 284,200 142,100 71,050 35,525 106,576 53,288 26,644 13,322 6,661 19,984 9,992 4,996 2,498 1,249 3,748 1,874 937 2,812 1,406 703 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511

More profiles

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