λ
Harmonic Matrix

6,817,840

24 × 5 × 85223
Abundant Even Composite

6,817,840 has digital root 7. The neighboring primes are 6817829 and 6817843; its proper-divisor sum differs from the starting integer by 2,215,984.

Prime Factor Structure

Factorization String 2^4 × 5 × 85223
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 15,851,664
Proper Divisor Sum 9,033,824
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #6817829 ← → #6817843

Radix Representation

Decimal 6817840
Binary 11010000000100000110000 (23 bits)
Octal 0o32004060
Hexadecimal 0x680830

Divisor Catalog (20)

1 2 4 5 8 10 16 20 40 80 85,223 170,446 340,892 426,115 681,784 852,230 1,363,568 1,704,460 3,408,920 6,817,840

Collatz Trajectory (222 steps to reach 1)

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

6,817,840 3,408,920 1,704,460 852,230 426,115 1,278,346 639,173 1,917,520 958,760 479,380 239,690 119,845 359,536 179,768 89,884 44,942 22,471 67,414 33,707 101,122 50,561 151,684 75,842 37,921 113,764 56,882 28,441 85,324 42,662 21,331 63,994 31,997 95,992 47,996 23,998 11,999 35,998 17,999 53,998 26,999 80,998 40,499 121,498 60,749 182,248 91,124 45,562 22,781 68,344 34,172 17,086 8,543 25,630 12,815 38,446 19,223 57,670 28,835 86,506 43,253

More profiles

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