λ
Harmonic Matrix

3,240,768

26 × 3 × 16879
Abundant Even Composite

3,240,768 has digital root 3. The neighboring primes are 3240767 and 3240841; its proper-divisor sum differs from the starting integer by 2,093,504.

Prime Factor Structure

Factorization String 2^6 × 3 × 16879
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 8,575,040
Proper Divisor Sum 5,334,272
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #3240767 ← → #3240841

Radix Representation

Decimal 3240768
Binary 1100010111001101000000 (22 bits)
Octal 0o14271500
Hexadecimal 0x317340

Divisor Catalog (28)

1 2 3 4 6 8 12 16 24 32 48 64 96 192 16,879 33,758 50,637 67,516 101,274 135,032 202,548 270,064 405,096 540,128 810,192 1,080,256 1,620,384 3,240,768

Collatz Trajectory (164 steps to reach 1)

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

3,240,768 1,620,384 810,192 405,096 202,548 101,274 50,637 151,912 75,956 37,978 18,989 56,968 28,484 14,242 7,121 21,364 10,682 5,341 16,024 8,012 4,006 2,003 6,010 3,005 9,016 4,508 2,254 1,127 3,382 1,691 5,074 2,537 7,612 3,806 1,903 5,710 2,855 8,566 4,283 12,850 6,425 19,276 9,638 4,819 14,458 7,229 21,688 10,844 5,422 2,711 8,134 4,067 12,202 6,101 18,304 9,152 4,576 2,288 1,144 572

More profiles

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