λ
Harmonic Matrix

222,147

32 × 24683
Deficient Odd Composite

222,147 has digital root 9. The neighboring primes are 222137 and 222149; its proper-divisor sum differs from the starting integer by -123,402.

Prime Factor Structure

Factorization String 3^2 × 24683
Distinct Prime Factors 2
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 6
Divisor Sum (σ) 320,892
Proper Divisor Sum 98,745
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #222137 ← → #222149

Radix Representation

Decimal 222147
Binary 110110001111000011 (18 bits)
Octal 0o661703
Hexadecimal 0x363C3

Divisor Catalog (6)

1 3 9 24,683 74,049 222,147

Collatz Trajectory (142 steps to reach 1)

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

222,147 666,442 333,221 999,664 499,832 249,916 124,958 62,479 187,438 93,719 281,158 140,579 421,738 210,869 632,608 316,304 158,152 79,076 39,538 19,769 59,308 29,654 14,827 44,482 22,241 66,724 33,362 16,681 50,044 25,022 12,511 37,534 18,767 56,302 28,151 84,454 42,227 126,682 63,341 190,024 95,012 47,506 23,753 71,260 35,630 17,815 53,446 26,723 80,170 40,085 120,256 60,128 30,064 15,032 7,516 3,758 1,879 5,638 2,819 8,458

More profiles

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