λ
Harmonic Matrix

334,710

2 × 32 × 5 × 3719
Abundant Even Composite

334,710 has digital root 9. The neighboring primes are 334699 and 334717; its proper-divisor sum differs from the starting integer by 201,060.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 3719
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 870,480
Proper Divisor Sum 535,770
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #334699 ← → #334717

Radix Representation

Decimal 334710
Binary 1010001101101110110 (19 bits)
Octal 0o1215566
Hexadecimal 0x51B76

Divisor Catalog (24)

1 2 3 5 6 9 10 15 18 30 45 90 3,719 7,438 11,157 18,595 22,314 33,471 37,190 55,785 66,942 111,570 167,355 334,710

Collatz Trajectory (153 steps to reach 1)

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

334,710 167,355 502,066 251,033 753,100 376,550 188,275 564,826 282,413 847,240 423,620 211,810 105,905 317,716 158,858 79,429 238,288 119,144 59,572 29,786 14,893 44,680 22,340 11,170 5,585 16,756 8,378 4,189 12,568 6,284 3,142 1,571 4,714 2,357 7,072 3,536 1,768 884 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364

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