λ
Harmonic Matrix

6,631,288

23 × 37 × 43 × 521
Deficient Even Composite

6,631,288 has digital root 7. The neighboring primes are 6631279 and 6631321; its proper-divisor sum differs from the starting integer by -170,816.

Prime Factor Structure

Factorization String 2^3 × 37 × 43 × 521
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 13,091,760
Proper Divisor Sum 6,460,472
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #6631279 ← → #6631321

Radix Representation

Decimal 6631288
Binary 11001010010111101111000 (23 bits)
Octal 0o31227570
Hexadecimal 0x652F78

Divisor Catalog (32)

1 2 4 8 37 43 74 86 148 172 296 344 521 1,042 1,591 2,084 3,182 4,168 6,364 12,728 19,277 22,403 38,554 44,806 77,108 89,612 154,216 179,224 828,911 1,657,822 3,315,644 6,631,288

Collatz Trajectory (116 steps to reach 1)

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

6,631,288 3,315,644 1,657,822 828,911 2,486,734 1,243,367 3,730,102 1,865,051 5,595,154 2,797,577 8,392,732 4,196,366 2,098,183 6,294,550 3,147,275 9,441,826 4,720,913 14,162,740 7,081,370 3,540,685 10,622,056 5,311,028 2,655,514 1,327,757 3,983,272 1,991,636 995,818 497,909 1,493,728 746,864 373,432 186,716 93,358 46,679 140,038 70,019 210,058 105,029 315,088 157,544 78,772 39,386 19,693 59,080 29,540 14,770 7,385 22,156 11,078 5,539 16,618 8,309 24,928 12,464 6,232 3,116 1,558 779 2,338 1,169

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