Harmonic Matrix

9,405,393

3 × 67 × 73 × 641

9,405,393 has digital root 6. The neighboring primes are 9405391 and 9405401; its proper-divisor sum differs from the starting integer by -5,888,610.

Prime Factor Structure

Factorization String 3 × 67 × 73 × 641

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 12,922,176

Proper Divisor Sum 3,516,783

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #9405391 ← → #9405401

Radix Representation

Decimal	9405393
Binary	100011111000001111010001 (24 bits)
Octal	0o43701721
Hexadecimal	0x8F83D1

Divisor Catalog (16)

1 3 67 73 201 219 641 1,923 4,891 14,673 42,947 46,793 128,841 140,379 3,135,131 9,405,393

Collatz Trajectory (181 steps to reach 1)

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

9,405,393 28,216,180 14,108,090 7,054,045 21,162,136 10,581,068 5,290,534 2,645,267 7,935,802 3,967,901 11,903,704 5,951,852 2,975,926 1,487,963 4,463,890 2,231,945 6,695,836 3,347,918 1,673,959 5,021,878 2,510,939 7,532,818 3,766,409 11,299,228 5,649,614 2,824,807 8,474,422 4,237,211 12,711,634 6,355,817 19,067,452 9,533,726 4,766,863 14,300,590 7,150,295 21,450,886 10,725,443 32,176,330 16,088,165 48,264,496 24,132,248 12,066,124 6,033,062 3,016,531 9,049,594 4,524,797 13,574,392 6,787,196 3,393,598 1,696,799 5,090,398 2,545,199 7,635,598 3,817,799 11,453,398 5,726,699 17,180,098 8,590,049 25,770,148 12,885,074

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