λ
Harmonic Matrix

7,823,442

2 × 3 × 11 × 113 × 1049
Abundant Even Composite

7,823,442 has digital root 3. The neighboring primes are 7823437 and 7823471; its proper-divisor sum differs from the starting integer by 1,589,916.

Prime Factor Structure

Factorization String 2 × 3 × 11 × 113 × 1049
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 17,236,800
Proper Divisor Sum 9,413,358
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #7823437 ← → #7823471

Radix Representation

Decimal 7823442
Binary 11101110110000001010010 (23 bits)
Octal 0o35660122
Hexadecimal 0x776052

Divisor Catalog (32)

1 2 3 6 11 22 33 66 113 226 339 678 1,049 1,243 2,098 2,486 3,147 3,729 6,294 7,458 11,539 23,078 34,617 69,234 118,537 237,074 355,611 711,222 1,303,907 2,607,814 3,911,721 7,823,442

Collatz Trajectory (204 steps to reach 1)

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

7,823,442 3,911,721 11,735,164 5,867,582 2,933,791 8,801,374 4,400,687 13,202,062 6,601,031 19,803,094 9,901,547 29,704,642 14,852,321 44,556,964 22,278,482 11,139,241 33,417,724 16,708,862 8,354,431 25,063,294 12,531,647 37,594,942 18,797,471 56,392,414 28,196,207 84,588,622 42,294,311 126,882,934 63,441,467 190,324,402 95,162,201 285,486,604 142,743,302 71,371,651 214,114,954 107,057,477 321,172,432 160,586,216 80,293,108 40,146,554 20,073,277 60,219,832 30,109,916 15,054,958 7,527,479 22,582,438 11,291,219 33,873,658 16,936,829 50,810,488 25,405,244 12,702,622 6,351,311 19,053,934 9,526,967 28,580,902 14,290,451 42,871,354 21,435,677 64,307,032

More profiles

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