λ
Harmonic Matrix

9,223,720

23 × 5 × 11 × 20963
Abundant Even Composite

9,223,720 has digital root 7. The neighboring primes are 9223679 and 9223733; its proper-divisor sum differs from the starting integer by 4,193,680.

Prime Factor Structure

Factorization String 2^3 × 5 × 11 × 20963
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 22,641,120
Proper Divisor Sum 13,417,400
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #9223679 ← → #9223733

Radix Representation

Decimal 9223720
Binary 100011001011111000101000 (24 bits)
Octal 0o43137050
Hexadecimal 0x8CBE28

Divisor Catalog (32)

1 2 4 5 8 10 11 20 22 40 44 55 88 110 220 440 20,963 41,926 83,852 104,815 167,704 209,630 230,593 419,260 461,186 838,520 922,372 1,152,965 1,844,744 2,305,930 4,611,860 9,223,720

Collatz Trajectory (88 steps to reach 1)

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

9,223,720 4,611,860 2,305,930 1,152,965 3,458,896 1,729,448 864,724 432,362 216,181 648,544 324,272 162,136 81,068 40,534 20,267 60,802 30,401 91,204 45,602 22,801 68,404 34,202 17,101 51,304 25,652 12,826 6,413 19,240 9,620 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640

More profiles

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