λ
Harmonic Matrix

2,190,191

2190191
Deficient Odd Prime

2,190,191 has digital root 5. The neighboring primes are 2190173 and 2190193; its proper-divisor sum differs from the starting integer by -2,190,190.

Prime Factor Structure

Factorization String 2190191
Distinct Prime Factors 1
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 2
Divisor Sum (σ) 2,190,192
Proper Divisor Sum 1
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #2190173 ← → #2190193

Radix Representation

Decimal 2190191
Binary 1000010110101101101111 (22 bits)
Octal 0o10265557
Hexadecimal 0x216B6F

Divisor Catalog (2)

Collatz Trajectory (197 steps to reach 1)

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

2,190,191 6,570,574 3,285,287 9,855,862 4,927,931 14,783,794 7,391,897 22,175,692 11,087,846 5,543,923 16,631,770 8,315,885 24,947,656 12,473,828 6,236,914 3,118,457 9,355,372 4,677,686 2,338,843 7,016,530 3,508,265 10,524,796 5,262,398 2,631,199 7,893,598 3,946,799 11,840,398 5,920,199 17,760,598 8,880,299 26,640,898 13,320,449 39,961,348 19,980,674 9,990,337 29,971,012 14,985,506 7,492,753 22,478,260 11,239,130 5,619,565 16,858,696 8,429,348 4,214,674 2,107,337 6,322,012 3,161,006 1,580,503 4,741,510 2,370,755 7,112,266 3,556,133 10,668,400 5,334,200 2,667,100 1,333,550 666,775 2,000,326 1,000,163 3,000,490

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