λ
Harmonic Matrix

243,309

3 × 11 × 73 × 101
Deficient Odd Composite

243,309 has digital root 3. The neighboring primes are 243301 and 243311; its proper-divisor sum differs from the starting integer by -124,314.

Prime Factor Structure

Factorization String 3 × 11 × 73 × 101
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 362,304
Proper Divisor Sum 118,995
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #243301 ← → #243311

Radix Representation

Decimal 243309
Binary 111011011001101101 (18 bits)
Octal 0o733155
Hexadecimal 0x3B66D

Divisor Catalog (16)

1 3 11 33 73 101 219 303 803 1,111 2,409 3,333 7,373 22,119 81,103 243,309

Collatz Trajectory (106 steps to reach 1)

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

243,309 729,928 364,964 182,482 91,241 273,724 136,862 68,431 205,294 102,647 307,942 153,971 461,914 230,957 692,872 346,436 173,218 86,609 259,828 129,914 64,957 194,872 97,436 48,718 24,359 73,078 36,539 109,618 54,809 164,428 82,214 41,107 123,322 61,661 184,984 92,492 46,246 23,123 69,370 34,685 104,056 52,028 26,014 13,007 39,022 19,511 58,534 29,267 87,802 43,901 131,704 65,852 32,926 16,463 49,390 24,695 74,086 37,043 111,130 55,565

More profiles

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