Harmonic Matrix

6,588,726

2 × 3 × 1098121

6,588,726 has digital root 6. The neighboring primes are 6588721 and 6588731; its proper-divisor sum differs from the starting integer by 12.

Prime Factor Structure

Factorization String 2 × 3 × 1098121

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 13,177,464

Proper Divisor Sum 6,588,738

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #6588721 ← → #6588731

Radix Representation

Decimal	6588726
Binary	11001001000100100110110 (23 bits)
Octal	0o31104466
Hexadecimal	0x648936

Divisor Catalog (8)

1 2 3 6 1,098,121 2,196,242 3,294,363 6,588,726

Collatz Trajectory (240 steps to reach 1)

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

6,588,726 3,294,363 9,883,090 4,941,545 14,824,636 7,412,318 3,706,159 11,118,478 5,559,239 16,677,718 8,338,859 25,016,578 12,508,289 37,524,868 18,762,434 9,381,217 28,143,652 14,071,826 7,035,913 21,107,740 10,553,870 5,276,935 15,830,806 7,915,403 23,746,210 11,873,105 35,619,316 17,809,658 8,904,829 26,714,488 13,357,244 6,678,622 3,339,311 10,017,934 5,008,967 15,026,902 7,513,451 22,540,354 11,270,177 33,810,532 16,905,266 8,452,633 25,357,900 12,678,950 6,339,475 19,018,426 9,509,213 28,527,640 14,263,820 7,131,910 3,565,955 10,697,866 5,348,933 16,046,800 8,023,400 4,011,700 2,005,850 1,002,925 3,008,776 1,504,388

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