λ
Harmonic Matrix

29,164

22 × 23 × 317
Deficient Even Composite

29,164 has digital root 4. The neighboring primes are 29153 and 29167; its proper-divisor sum differs from the starting integer by -4,904.

Prime Factor Structure

Factorization String 2^2 × 23 × 317
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 53,424
Proper Divisor Sum 24,260
Digit Sum / Digital Root 22 (Root: 4)
Adjacent Primes #29153 ← → #29167

Radix Representation

Decimal 29164
Binary 111000111101100 (15 bits)
Octal 0o70754
Hexadecimal 0x71EC

Divisor Catalog (12)

1 2 4 23 46 92 317 634 1,268 7,291 14,582 29,164

Collatz Trajectory (165 steps to reach 1)

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

29,164 14,582 7,291 21,874 10,937 32,812 16,406 8,203 24,610 12,305 36,916 18,458 9,229 27,688 13,844 6,922 3,461 10,384 5,192 2,596 1,298 649 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235 3,706 1,853 5,560 2,780 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762 881 2,644 1,322 661 1,984 992 496 248 124 62 31

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