λ
Harmonic Matrix

1,021,440

29 × 3 × 5 × 7 × 19
Abundant Even Composite

1,021,440 has digital root 3. The neighboring primes are 1021429 and 1021441; its proper-divisor sum differs from the starting integer by 1,885,440.

Prime Factor Structure

Factorization String 2^9 × 3 × 5 × 7 × 19
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 160
Divisor Sum (σ) 3,928,320
Proper Divisor Sum 2,906,880
Digit Sum / Digital Root 12 (Root: 3)
Adjacent Primes #1021429 ← → #1021441

Radix Representation

Decimal 1021440
Binary 11111001011000000000 (20 bits)
Octal 0o3713000
Hexadecimal 0xF9600

Divisor Catalog (60 of 160)

1 2 3 4 5 6 7 8 10 12 14 15 16 19 20 21 24 28 30 32 35 38 40 42 48 56 57 60 64 70 76 80 84 95 96 105 112 114 120 128 133 140 152 160 168 190 192 210 224 228 240 256 266 280 285 304 320 336 380 384

Collatz Trajectory (59 steps to reach 1)

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

1,021,440 510,720 255,360 127,680 63,840 31,920 15,960 7,980 3,990 1,995 5,986 2,993 8,980 4,490 2,245 6,736 3,368 1,684 842 421 1,264 632 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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