λ
Harmonic Matrix

1,403,946

2 × 33 × 25999
Abundant Even Composite

1,403,946 has digital root 9. The neighboring primes are 1403939 and 1403951; its proper-divisor sum differs from the starting integer by 312,108.

Prime Factor Structure

Factorization String 2 × 3^3 × 25999
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 3,120,000
Proper Divisor Sum 1,716,054
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #1403939 ← → #1403951

Radix Representation

Decimal 1403946
Binary 101010110110000101010 (21 bits)
Octal 0o5266052
Hexadecimal 0x156C2A

Divisor Catalog (16)

1 2 3 6 9 18 27 54 25,999 51,998 77,997 155,994 233,991 467,982 701,973 1,403,946

Collatz Trajectory (199 steps to reach 1)

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

1,403,946 701,973 2,105,920 1,052,960 526,480 263,240 131,620 65,810 32,905 98,716 49,358 24,679 74,038 37,019 111,058 55,529 166,588 83,294 41,647 124,942 62,471 187,414 93,707 281,122 140,561 421,684 210,842 105,421 316,264 158,132 79,066 39,533 118,600 59,300 29,650 14,825 44,476 22,238 11,119 33,358 16,679 50,038 25,019 75,058 37,529 112,588 56,294 28,147 84,442 42,221 126,664 63,332 31,666 15,833 47,500 23,750 11,875 35,626 17,813 53,440

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