λ
Harmonic Matrix

9,769,080

23 × 3 × 5 × 81409
Abundant Even Composite

9,769,080 has digital root 3. The neighboring primes are 9769049 and 9769087; its proper-divisor sum differs from the starting integer by 9,769,440.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 81409
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 29,307,600
Proper Divisor Sum 19,538,520
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #9769049 ← → #9769087

Radix Representation

Decimal 9769080
Binary 100101010001000001111000 (24 bits)
Octal 0o45210170
Hexadecimal 0x951078

Divisor Catalog (32)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 81,409 162,818 244,227 325,636 407,045 488,454 651,272 814,090 976,908 1,221,135 1,628,180 1,953,816 2,442,270 3,256,360 4,884,540 9,769,080

Collatz Trajectory (145 steps to reach 1)

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

9,769,080 4,884,540 2,442,270 1,221,135 3,663,406 1,831,703 5,495,110 2,747,555 8,242,666 4,121,333 12,364,000 6,182,000 3,091,000 1,545,500 772,750 386,375 1,159,126 579,563 1,738,690 869,345 2,608,036 1,304,018 652,009 1,956,028 978,014 489,007 1,467,022 733,511 2,200,534 1,100,267 3,300,802 1,650,401 4,951,204 2,475,602 1,237,801 3,713,404 1,856,702 928,351 2,785,054 1,392,527 4,177,582 2,088,791 6,266,374 3,133,187 9,399,562 4,699,781 14,099,344 7,049,672 3,524,836 1,762,418 881,209 2,643,628 1,321,814 660,907 1,982,722 991,361 2,974,084 1,487,042 743,521 2,230,564

More profiles

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