λ
Harmonic Matrix

8,230,960

24 × 5 × 137 × 751
Abundant Even Composite

8,230,960 has digital root 1. The neighboring primes are 8230951 and 8230967; its proper-divisor sum differs from the starting integer by 2,840,416.

Prime Factor Structure

Factorization String 2^4 × 5 × 137 × 751
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 19,302,336
Proper Divisor Sum 11,071,376
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #8230951 ← → #8230967

Radix Representation

Decimal 8230960
Binary 11111011001100000110000 (23 bits)
Octal 0o37314060
Hexadecimal 0x7D9830

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 80 137 274 548 685 751 1,096 1,370 1,502 2,192 2,740 3,004 3,755 5,480 6,008 7,510 10,960 12,016 15,020 30,040 60,080 102,887 205,774 411,548 514,435 823,096 1,028,870 1,646,192 2,057,740 4,115,480 8,230,960

Collatz Trajectory (199 steps to reach 1)

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

8,230,960 4,115,480 2,057,740 1,028,870 514,435 1,543,306 771,653 2,314,960 1,157,480 578,740 289,370 144,685 434,056 217,028 108,514 54,257 162,772 81,386 40,693 122,080 61,040 30,520 15,260 7,630 3,815 11,446 5,723 17,170 8,585 25,756 12,878 6,439 19,318 9,659 28,978 14,489 43,468 21,734 10,867 32,602 16,301 48,904 24,452 12,226 6,113 18,340 9,170 4,585 13,756 6,878 3,439 10,318 5,159 15,478 7,739 23,218 11,609 34,828 17,414 8,707

More profiles

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