λ
Harmonic Matrix

9,027,024

24 × 3 × 61 × 3083
Abundant Even Composite

9,027,024 has digital root 6. The neighboring primes are 9026987 and 9027043; its proper-divisor sum differs from the starting integer by 5,655,744.

Prime Factor Structure

Factorization String 2^4 × 3 × 61 × 3083
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 23,709,792
Proper Divisor Sum 14,682,768
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #9026987 ← → #9027043

Radix Representation

Decimal 9027024
Binary 100010011011110111010000 (24 bits)
Octal 0o42336720
Hexadecimal 0x89BDD0

Divisor Catalog (40)

1 2 3 4 6 8 12 16 24 48 61 122 183 244 366 488 732 976 1,464 2,928 3,083 6,166 9,249 12,332 18,498 24,664 36,996 49,328 73,992 147,984 188,063 376,126 564,189 752,252 1,128,378 1,504,504 2,256,756 3,009,008 4,513,512 9,027,024

Collatz Trajectory (256 steps to reach 1)

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

9,027,024 4,513,512 2,256,756 1,128,378 564,189 1,692,568 846,284 423,142 211,571 634,714 317,357 952,072 476,036 238,018 119,009 357,028 178,514 89,257 267,772 133,886 66,943 200,830 100,415 301,246 150,623 451,870 225,935 677,806 338,903 1,016,710 508,355 1,525,066 762,533 2,287,600 1,143,800 571,900 285,950 142,975 428,926 214,463 643,390 321,695 965,086 482,543 1,447,630 723,815 2,171,446 1,085,723 3,257,170 1,628,585 4,885,756 2,442,878 1,221,439 3,664,318 1,832,159 5,496,478 2,748,239 8,244,718 4,122,359 12,367,078

More profiles

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