λ
Harmonic Matrix

1,434,120

23 × 3 × 5 × 17 × 19 × 37
Abundant Even Composite

1,434,120 has digital root 6. The neighboring primes are 1434109 and 1434131; its proper-divisor sum differs from the starting integer by 2,056,560.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 17 × 19 × 37
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 128
Divisor Sum (σ) 4,924,800
Proper Divisor Sum 3,490,680
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #1434109 ← → #1434131

Radix Representation

Decimal 1434120
Binary 101011110001000001000 (21 bits)
Octal 0o5361010
Hexadecimal 0x15E208

Divisor Catalog (60 of 128)

1 2 3 4 5 6 8 10 12 15 17 19 20 24 30 34 37 38 40 51 57 60 68 74 76 85 95 102 111 114 120 136 148 152 170 185 190 204 222 228 255 285 296 323 340 370 380 408 444 456 510 555 570 629 646 680 703 740 760 888

Collatz Trajectory (75 steps to reach 1)

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

1,434,120 717,060 358,530 179,265 537,796 268,898 134,449 403,348 201,674 100,837 302,512 151,256 75,628 37,814 18,907 56,722 28,361 85,084 42,542 21,271 63,814 31,907 95,722 47,861 143,584 71,792 35,896 17,948 8,974 4,487 13,462 6,731 20,194 10,097 30,292 15,146 7,573 22,720 11,360 5,680 2,840 1,420 710 355 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44

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