λ
Harmonic Matrix

6,769,821

3 × 227 × 9941
Deficient Odd Composite

6,769,821 has digital root 3. The neighboring primes are 6769817 and 6769831; its proper-divisor sum differs from the starting integer by -4,472,538.

Prime Factor Structure

Factorization String 3 × 227 × 9941
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 9,067,104
Proper Divisor Sum 2,297,283
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #6769817 ← → #6769831

Radix Representation

Decimal 6769821
Binary 11001110100110010011101 (23 bits)
Octal 0o31646235
Hexadecimal 0x674C9D

Divisor Catalog (8)

1 3 227 681 9,941 29,823 2,256,607 6,769,821

Collatz Trajectory (134 steps to reach 1)

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

6,769,821 20,309,464 10,154,732 5,077,366 2,538,683 7,616,050 3,808,025 11,424,076 5,712,038 2,856,019 8,568,058 4,284,029 12,852,088 6,426,044 3,213,022 1,606,511 4,819,534 2,409,767 7,229,302 3,614,651 10,843,954 5,421,977 16,265,932 8,132,966 4,066,483 12,199,450 6,099,725 18,299,176 9,149,588 4,574,794 2,287,397 6,862,192 3,431,096 1,715,548 857,774 428,887 1,286,662 643,331 1,929,994 964,997 2,894,992 1,447,496 723,748 361,874 180,937 542,812 271,406 135,703 407,110 203,555 610,666 305,333 916,000 458,000 229,000 114,500 57,250 28,625 85,876 42,938

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