λ
Harmonic Matrix

314,442

2 × 35 × 647
Abundant Even Composite

314,442 has digital root 9. The neighboring primes are 314441 and 314453; its proper-divisor sum differs from the starting integer by 78,732.

Prime Factor Structure

Factorization String 2 × 3^5 × 647
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 707,616
Proper Divisor Sum 393,174
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #314441 ← → #314453

Radix Representation

Decimal 314442
Binary 1001100110001001010 (19 bits)
Octal 0o1146112
Hexadecimal 0x4CC4A

Divisor Catalog (24)

1 2 3 6 9 18 27 54 81 162 243 486 647 1,294 1,941 3,882 5,823 11,646 17,469 34,938 52,407 104,814 157,221 314,442

Collatz Trajectory (109 steps to reach 1)

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

314,442 157,221 471,664 235,832 117,916 58,958 29,479 88,438 44,219 132,658 66,329 198,988 99,494 49,747 149,242 74,621 223,864 111,932 55,966 27,983 83,950 41,975 125,926 62,963 188,890 94,445 283,336 141,668 70,834 35,417 106,252 53,126 26,563 79,690 39,845 119,536 59,768 29,884 14,942 7,471 22,414 11,207 33,622 16,811 50,434 25,217 75,652 37,826 18,913 56,740 28,370 14,185 42,556 21,278 10,639 31,918 15,959 47,878 23,939 71,818

More profiles

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