λ
Harmonic Matrix
Atlas › Integer Profiles › Node 8,423,992

8,423,992

23 × 19 × 157 × 353
Deficient Even Composite

8,423,992 has digital root 1. The neighboring primes are 8423953 and 8423999; its proper-divisor sum differs from the starting integer by -68,384.

Prime Factor Structure

Factorization String 2^3 × 19 × 157 × 353
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 16,779,600
Proper Divisor Sum 8,355,608
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #8423953 ← → #8423999

Radix Representation

Decimal 8423992
Binary 100000001000101000111000 (24 bits)
Octal 0o40105070
Hexadecimal 0x808A38

Divisor Catalog (32)

1 2 4 8 19 38 76 152 157 314 353 628 706 1,256 1,412 2,824 2,983 5,966 6,707 11,932 13,414 23,864 26,828 53,656 55,421 110,842 221,684 443,368 1,052,999 2,105,998 4,211,996 8,423,992

Collatz Trajectory (243 steps to reach 1)

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

8,423,992 4,211,996 2,105,998 1,052,999 3,158,998 1,579,499 4,738,498 2,369,249 7,107,748 3,553,874 1,776,937 5,330,812 2,665,406 1,332,703 3,998,110 1,999,055 5,997,166 2,998,583 8,995,750 4,497,875 13,493,626 6,746,813 20,240,440 10,120,220 5,060,110 2,530,055 7,590,166 3,795,083 11,385,250 5,692,625 17,077,876 8,538,938 4,269,469 12,808,408 6,404,204 3,202,102 1,601,051 4,803,154 2,401,577 7,204,732 3,602,366 1,801,183 5,403,550 2,701,775 8,105,326 4,052,663 12,157,990 6,078,995 18,236,986 9,118,493 27,355,480 13,677,740 6,838,870 3,419,435 10,258,306 5,129,153 15,387,460 7,693,730 3,846,865 11,540,596

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