λ
Harmonic Matrix

3,829,392

24 × 32 × 7 × 29 × 131
Abundant Even Composite

3,829,392 has digital root 9. The neighboring primes are 3829391 and 3829429; its proper-divisor sum differs from the starting integer by 5,108,256.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 7 × 29 × 131
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 120
Divisor Sum (σ) 12,767,040
Proper Divisor Sum 8,937,648
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #3829391 ← → #3829429

Radix Representation

Decimal 3829392
Binary 1110100110111010010000 (22 bits)
Octal 0o16467220
Hexadecimal 0x3A6E90

Divisor Catalog (60 of 120)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 29 36 42 48 56 58 63 72 84 87 112 116 126 131 144 168 174 203 232 252 261 262 336 348 393 406 464 504 522 524 609 696 786 812 917 1,008 1,044 1,048 1,179 1,218 1,392 1,572 1,624 1,827 1,834

Collatz Trajectory (110 steps to reach 1)

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

3,829,392 1,914,696 957,348 478,674 239,337 718,012 359,006 179,503 538,510 269,255 807,766 403,883 1,211,650 605,825 1,817,476 908,738 454,369 1,363,108 681,554 340,777 1,022,332 511,166 255,583 766,750 383,375 1,150,126 575,063 1,725,190 862,595 2,587,786 1,293,893 3,881,680 1,940,840 970,420 485,210 242,605 727,816 363,908 181,954 90,977 272,932 136,466 68,233 204,700 102,350 51,175 153,526 76,763 230,290 115,145 345,436 172,718 86,359 259,078 129,539 388,618 194,309 582,928 291,464 145,732

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