λ
Harmonic Matrix

3,764,640

25 × 3 × 5 × 11 × 23 × 31
Abundant Even Composite

3,764,640 has digital root 3. The neighboring primes are 3764597 and 3764647; its proper-divisor sum differs from the starting integer by 6,405,312.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 11 × 23 × 31
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 192
Divisor Sum (σ) 13,934,592
Proper Divisor Sum 10,169,952
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #3764597 ← → #3764647

Radix Representation

Decimal 3764640
Binary 1110010111000110100000 (22 bits)
Octal 0o16270640
Hexadecimal 0x3971A0

Divisor Catalog (60 of 192)

1 2 3 4 5 6 8 10 11 12 15 16 20 22 23 24 30 31 32 33 40 44 46 48 55 60 62 66 69 80 88 92 93 96 110 115 120 124 132 138 155 160 165 176 184 186 220 230 240 248 253 264 276 310 330 341 345 352 368 372

Collatz Trajectory (141 steps to reach 1)

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

3,764,640 1,882,320 941,160 470,580 235,290 117,645 352,936 176,468 88,234 44,117 132,352 66,176 33,088 16,544 8,272 4,136 2,068 1,034 517 1,552 776 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700

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