λ
Harmonic Matrix

6,682,326

2 × 3 × 73 × 17 × 191
Abundant Even Composite

6,682,326 has digital root 6. The neighboring primes are 6682301 and 6682327; its proper-divisor sum differs from the starting integer by 3,224,148.

Prime Factor Structure

Factorization String 2 × 3 × 7^3 × 17 × 191
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 16,588,800
Proper Divisor Sum 9,906,474
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #6682301 ← → #6682327

Radix Representation

Decimal 6682326
Binary 11001011111011011010110 (23 bits)
Octal 0o31373326
Hexadecimal 0x65F6D6

Divisor Catalog (60 of 64)

1 2 3 6 7 14 17 21 34 42 49 51 98 102 119 147 191 238 294 343 357 382 573 686 714 833 1,029 1,146 1,337 1,666 2,058 2,499 2,674 3,247 4,011 4,998 5,831 6,494 8,022 9,359 9,741 11,662 17,493 18,718 19,482 22,729 28,077 34,986 45,458 56,154 65,513 68,187 131,026 136,374 159,103 196,539 318,206 393,078 477,309 954,618

Collatz Trajectory (59 steps to reach 1)

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

6,682,326 3,341,163 10,023,490 5,011,745 15,035,236 7,517,618 3,758,809 11,276,428 5,638,214 2,819,107 8,457,322 4,228,661 12,685,984 6,342,992 3,171,496 1,585,748 792,874 396,437 1,189,312 594,656 297,328 148,664 74,332 37,166 18,583 55,750 27,875 83,626 41,813 125,440 62,720 31,360 15,680 7,840 3,920 1,960 980 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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