λ
Harmonic Matrix

8,990,046

2 × 32 × 13 × 103 × 373
Abundant Even Composite

8,990,046 has digital root 9. The neighboring primes are 8990041 and 8990063; its proper-divisor sum differs from the starting integer by 3,257,124.

Prime Factor Structure

Factorization String 2 × 3^2 × 13 × 103 × 373
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,237,216
Proper Divisor Sum 12,247,170
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8990041 ← → #8990063

Radix Representation

Decimal 8990046
Binary 100010010010110101011110 (24 bits)
Octal 0o42226536
Hexadecimal 0x892D5E

Divisor Catalog (48)

1 2 3 6 9 13 18 26 39 78 103 117 206 234 309 373 618 746 927 1,119 1,339 1,854 2,238 2,678 3,357 4,017 4,849 6,714 8,034 9,698 12,051 14,547 24,102 29,094 38,419 43,641 76,838 87,282 115,257 230,514 345,771 499,447 691,542 998,894 1,498,341 2,996,682 4,495,023 8,990,046

Collatz Trajectory (212 steps to reach 1)

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

8,990,046 4,495,023 13,485,070 6,742,535 20,227,606 10,113,803 30,341,410 15,170,705 45,512,116 22,756,058 11,378,029 34,134,088 17,067,044 8,533,522 4,266,761 12,800,284 6,400,142 3,200,071 9,600,214 4,800,107 14,400,322 7,200,161 21,600,484 10,800,242 5,400,121 16,200,364 8,100,182 4,050,091 12,150,274 6,075,137 18,225,412 9,112,706 4,556,353 13,669,060 6,834,530 3,417,265 10,251,796 5,125,898 2,562,949 7,688,848 3,844,424 1,922,212 961,106 480,553 1,441,660 720,830 360,415 1,081,246 540,623 1,621,870 810,935 2,432,806 1,216,403 3,649,210 1,824,605 5,473,816 2,736,908 1,368,454 684,227 2,052,682

More profiles

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