λ
Harmonic Matrix

165,419

83 × 1993
Deficient Odd Composite

165,419 has digital root 8. The neighboring primes are 165397 and 165437; its proper-divisor sum differs from the starting integer by -163,342.

Prime Factor Structure

Factorization String 83 × 1993
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 4
Divisor Sum (σ) 167,496
Proper Divisor Sum 2,077
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #165397 ← → #165437

Radix Representation

Decimal 165419
Binary 101000011000101011 (18 bits)
Octal 0o503053
Hexadecimal 0x2862B

Divisor Catalog (4)

1 83 1,993 165,419

Collatz Trajectory (152 steps to reach 1)

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

165,419 496,258 248,129 744,388 372,194 186,097 558,292 279,146 139,573 418,720 209,360 104,680 52,340 26,170 13,085 39,256 19,628 9,814 4,907 14,722 7,361 22,084 11,042 5,521 16,564 8,282 4,141 12,424 6,212 3,106 1,553 4,660 2,330 1,165 3,496 1,748 874 437 1,312 656 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182

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