λ
Harmonic Matrix

1,561,782

2 × 3 × 131 × 1987
Abundant Even Composite

1,561,782 has digital root 3. The neighboring primes are 1561759 and 1561801; its proper-divisor sum differs from the starting integer by 25,428.

Prime Factor Structure

Factorization String 2 × 3 × 131 × 1987
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 16
Divisor Sum (σ) 3,148,992
Proper Divisor Sum 1,587,210
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #1561759 ← → #1561801

Radix Representation

Decimal 1561782
Binary 101111101010010110110 (21 bits)
Octal 0o5752266
Hexadecimal 0x17D4B6

Divisor Catalog (16)

1 2 3 6 131 262 393 786 1,987 3,974 5,961 11,922 260,297 520,594 780,891 1,561,782

Collatz Trajectory (194 steps to reach 1)

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

1,561,782 780,891 2,342,674 1,171,337 3,514,012 1,757,006 878,503 2,635,510 1,317,755 3,953,266 1,976,633 5,929,900 2,964,950 1,482,475 4,447,426 2,223,713 6,671,140 3,335,570 1,667,785 5,003,356 2,501,678 1,250,839 3,752,518 1,876,259 5,628,778 2,814,389 8,443,168 4,221,584 2,110,792 1,055,396 527,698 263,849 791,548 395,774 197,887 593,662 296,831 890,494 445,247 1,335,742 667,871 2,003,614 1,001,807 3,005,422 1,502,711 4,508,134 2,254,067 6,762,202 3,381,101 10,143,304 5,071,652 2,535,826 1,267,913 3,803,740 1,901,870 950,935 2,852,806 1,426,403 4,279,210 2,139,605

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