λ
Harmonic Matrix

8,401,874

2 × 13 × 323149
Deficient Even Composite

8,401,874 has digital root 5. The neighboring primes are 8401873 and 8401901; its proper-divisor sum differs from the starting integer by -3,231,448.

Prime Factor Structure

Factorization String 2 × 13 × 323149
Distinct Prime Factors 3
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 8
Divisor Sum (σ) 13,572,300
Proper Divisor Sum 5,170,426
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8401873 ← → #8401901

Radix Representation

Decimal 8401874
Binary 100000000011001111010010 (24 bits)
Octal 0o40031722
Hexadecimal 0x8033D2

Divisor Catalog (8)

1 2 13 26 323,149 646,298 4,200,937 8,401,874

Collatz Trajectory (230 steps to reach 1)

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

8,401,874 4,200,937 12,602,812 6,301,406 3,150,703 9,452,110 4,726,055 14,178,166 7,089,083 21,267,250 10,633,625 31,900,876 15,950,438 7,975,219 23,925,658 11,962,829 35,888,488 17,944,244 8,972,122 4,486,061 13,458,184 6,729,092 3,364,546 1,682,273 5,046,820 2,523,410 1,261,705 3,785,116 1,892,558 946,279 2,838,838 1,419,419 4,258,258 2,129,129 6,387,388 3,193,694 1,596,847 4,790,542 2,395,271 7,185,814 3,592,907 10,778,722 5,389,361 16,168,084 8,084,042 4,042,021 12,126,064 6,063,032 3,031,516 1,515,758 757,879 2,273,638 1,136,819 3,410,458 1,705,229 5,115,688 2,557,844 1,278,922 639,461 1,918,384

More profiles

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