λ
Harmonic Matrix

2,206,240

25 × 5 × 13789
Abundant Even Composite

2,206,240 has digital root 7. The neighboring primes are 2206219 and 2206247; its proper-divisor sum differs from the starting integer by 800,140.

Prime Factor Structure

Factorization String 2^5 × 5 × 13789
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 5,212,620
Proper Divisor Sum 3,006,380
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #2206219 ← → #2206247

Radix Representation

Decimal 2206240
Binary 1000011010101000100000 (22 bits)
Octal 0o10325040
Hexadecimal 0x21AA20

Divisor Catalog (24)

1 2 4 5 8 10 16 20 32 40 80 160 13,789 27,578 55,156 68,945 110,312 137,890 220,624 275,780 441,248 551,560 1,103,120 2,206,240

Collatz Trajectory (91 steps to reach 1)

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

2,206,240 1,103,120 551,560 275,780 137,890 68,945 206,836 103,418 51,709 155,128 77,564 38,782 19,391 58,174 29,087 87,262 43,631 130,894 65,447 196,342 98,171 294,514 147,257 441,772 220,886 110,443 331,330 165,665 496,996 248,498 124,249 372,748 186,374 93,187 279,562 139,781 419,344 209,672 104,836 52,418 26,209 78,628 39,314 19,657 58,972 29,486 14,743 44,230 22,115 66,346 33,173 99,520 49,760 24,880 12,440 6,220 3,110 1,555 4,666 2,333

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