λ
Harmonic Matrix

5,311,323

32 × 31 × 19037
Deficient Odd Composite

5,311,323 has digital root 9. The neighboring primes are 5311307 and 5311337; its proper-divisor sum differs from the starting integer by -2,702,838.

Prime Factor Structure

Factorization String 3^2 × 31 × 19037
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 7,919,808
Proper Divisor Sum 2,608,485
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #5311307 ← → #5311337

Radix Representation

Decimal 5311323
Binary 10100010000101101011011 (23 bits)
Octal 0o24205533
Hexadecimal 0x510B5B

Divisor Catalog (12)

1 3 9 31 93 279 19,037 57,111 171,333 590,147 1,770,441 5,311,323

Collatz Trajectory (263 steps to reach 1)

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

5,311,323 15,933,970 7,966,985 23,900,956 11,950,478 5,975,239 17,925,718 8,962,859 26,888,578 13,444,289 40,332,868 20,166,434 10,083,217 30,249,652 15,124,826 7,562,413 22,687,240 11,343,620 5,671,810 2,835,905 8,507,716 4,253,858 2,126,929 6,380,788 3,190,394 1,595,197 4,785,592 2,392,796 1,196,398 598,199 1,794,598 897,299 2,691,898 1,345,949 4,037,848 2,018,924 1,009,462 504,731 1,514,194 757,097 2,271,292 1,135,646 567,823 1,703,470 851,735 2,555,206 1,277,603 3,832,810 1,916,405 5,749,216 2,874,608 1,437,304 718,652 359,326 179,663 538,990 269,495 808,486 404,243 1,212,730

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