λ
Harmonic Matrix

343,199

343199
Deficient Odd Prime

343,199 has digital root 2. The neighboring primes are 343193 and 343219; its proper-divisor sum differs from the starting integer by -343,198.

Prime Factor Structure

Factorization String 343199
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 343,200
Proper Divisor Sum 1
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #343193 ← → #343219

Radix Representation

Decimal 343199
Binary 1010011110010011111 (19 bits)
Octal 0o1236237
Hexadecimal 0x53C9F

Divisor Catalog (2)

1 343,199

Collatz Trajectory (241 steps to reach 1)

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

343,199 1,029,598 514,799 1,544,398 772,199 2,316,598 1,158,299 3,474,898 1,737,449 5,212,348 2,606,174 1,303,087 3,909,262 1,954,631 5,863,894 2,931,947 8,795,842 4,397,921 13,193,764 6,596,882 3,298,441 9,895,324 4,947,662 2,473,831 7,421,494 3,710,747 11,132,242 5,566,121 16,698,364 8,349,182 4,174,591 12,523,774 6,261,887 18,785,662 9,392,831 28,178,494 14,089,247 42,267,742 21,133,871 63,401,614 31,700,807 95,102,422 47,551,211 142,653,634 71,326,817 213,980,452 106,990,226 53,495,113 160,485,340 80,242,670 40,121,335 120,364,006 60,182,003 180,546,010 90,273,005 270,819,016 135,409,508 67,704,754 33,852,377 101,557,132

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