λ
Harmonic Matrix

9,426,144

25 × 3 × 7 × 132 × 83
Abundant Even Composite

9,426,144 has digital root 3. The neighboring primes are 9426107 and 9426161; its proper-divisor sum differs from the starting integer by 12,137,664.

Prime Factor Structure

Factorization String 2^5 × 3 × 7 × 13^2 × 83
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 144
Divisor Sum (σ) 30,989,952
Proper Divisor Sum 21,563,808
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #9426107 ← → #9426161

Radix Representation

Decimal 9426144
Binary 100011111101010011100000 (24 bits)
Octal 0o43752340
Hexadecimal 0x8FD4E0

Divisor Catalog (60 of 144)

1 2 3 4 6 7 8 12 13 14 16 21 24 26 28 32 39 42 48 52 56 78 83 84 91 96 104 112 156 166 168 169 182 208 224 249 273 312 332 336 338 364 416 498 507 546 581 624 664 672 676 728 996 1,014 1,079 1,092 1,162 1,183 1,248 1,328

Collatz Trajectory (176 steps to reach 1)

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

9,426,144 4,713,072 2,356,536 1,178,268 589,134 294,567 883,702 441,851 1,325,554 662,777 1,988,332 994,166 497,083 1,491,250 745,625 2,236,876 1,118,438 559,219 1,677,658 838,829 2,516,488 1,258,244 629,122 314,561 943,684 471,842 235,921 707,764 353,882 176,941 530,824 265,412 132,706 66,353 199,060 99,530 49,765 149,296 74,648 37,324 18,662 9,331 27,994 13,997 41,992 20,996 10,498 5,249 15,748 7,874 3,937 11,812 5,906 2,953 8,860 4,430 2,215 6,646 3,323 9,970

More profiles

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