λ
Harmonic Matrix

122,968

23 × 19 × 809
Deficient Even Composite

122,968 has digital root 1. The neighboring primes are 122963 and 122971; its proper-divisor sum differs from the starting integer by -2,936.

Prime Factor Structure

Factorization String 2^3 × 19 × 809
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 243,000
Proper Divisor Sum 120,032
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #122963 ← → #122971

Radix Representation

Decimal 122968
Binary 11110000001011000 (17 bits)
Octal 0o360130
Hexadecimal 0x1E058

Divisor Catalog (16)

1 2 4 8 19 38 76 152 809 1,618 3,236 6,472 15,371 30,742 61,484 122,968

Collatz Trajectory (43 steps to reach 1)

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

122,968 61,484 30,742 15,371 46,114 23,057 69,172 34,586 17,293 51,880 25,940 12,970 6,485 19,456 9,728 4,864 2,432 1,216 608 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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