λ
Harmonic Matrix

708,813

32 × 7 × 11251
Deficient Odd Composite

708,813 has digital root 9. The neighboring primes are 708803 and 708823; its proper-divisor sum differs from the starting integer by -247,418.

Prime Factor Structure

Factorization String 3^2 × 7 × 11251
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 1,170,208
Proper Divisor Sum 461,395
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #708803 ← → #708823

Radix Representation

Decimal 708813
Binary 10101101000011001101 (20 bits)
Octal 0o2550315
Hexadecimal 0xAD0CD

Divisor Catalog (12)

1 3 7 9 21 63 11,251 33,753 78,757 101,259 236,271 708,813

Collatz Trajectory (48 steps to reach 1)

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

708,813 2,126,440 1,063,220 531,610 265,805 797,416 398,708 199,354 99,677 299,032 149,516 74,758 37,379 112,138 56,069 168,208 84,104 42,052 21,026 10,513 31,540 15,770 7,885 23,656 11,828 5,914 2,957 8,872 4,436 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16 8 4 2 1

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