λ
Harmonic Matrix

751,709

72 × 232 × 29
Deficient Odd Composite

751,709 has digital root 2. The neighboring primes are 751691 and 751711; its proper-divisor sum differs from the starting integer by -557,788.

Prime Factor Structure

Factorization String 7^2 × 23^2 × 29
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 18
Divisor Sum (σ) 945,630
Proper Divisor Sum 193,921
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #751691 ← → #751711

Radix Representation

Decimal 751709
Binary 10110111100001011101 (20 bits)
Octal 0o2674135
Hexadecimal 0xB785D

Divisor Catalog (18)

1 7 23 29 49 161 203 529 667 1,127 1,421 3,703 4,669 15,341 25,921 32,683 107,387 751,709

Collatz Trajectory (56 steps to reach 1)

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

751,709 2,255,128 1,127,564 563,782 281,891 845,674 422,837 1,268,512 634,256 317,128 158,564 79,282 39,641 118,924 59,462 29,731 89,194 44,597 133,792 66,896 33,448 16,724 8,362 4,181 12,544 6,272 3,136 1,568 784 392 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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