λ
Harmonic Matrix

72,808

23 × 19 × 479
Deficient Even Composite

72,808 has digital root 7. The neighboring primes are 72797 and 72817; its proper-divisor sum differs from the starting integer by -1,616.

Prime Factor Structure

Factorization String 2^3 × 19 × 479
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 144,000
Proper Divisor Sum 71,192
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #72797 ← → #72817

Radix Representation

Decimal 72808
Binary 10001110001101000 (17 bits)
Octal 0o216150
Hexadecimal 0x11C68

Divisor Catalog (16)

1 2 4 8 19 38 76 152 479 958 1,916 3,832 9,101 18,202 36,404 72,808

Collatz Trajectory (24 steps to reach 1)

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

72,808 36,404 18,202 9,101 27,304 13,652 6,826 3,413 10,240 5,120 2,560 1,280 640 320 160 80 40 20 10 5 16 8 4 2 1

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