λ
Harmonic Matrix

1,976,526

2 × 32 × 109807
Abundant Even Composite

1,976,526 has digital root 9. The neighboring primes are 1976519 and 1976537; its proper-divisor sum differs from the starting integer by 329,460.

Prime Factor Structure

Factorization String 2 × 3^2 × 109807
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 4,282,512
Proper Divisor Sum 2,305,986
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #1976519 ← → #1976537

Radix Representation

Decimal 1976526
Binary 111100010100011001110 (21 bits)
Octal 0o7424316
Hexadecimal 0x1E28CE

Divisor Catalog (12)

1 2 3 6 9 18 109,807 219,614 329,421 658,842 988,263 1,976,526

Collatz Trajectory (145 steps to reach 1)

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

1,976,526 988,263 2,964,790 1,482,395 4,447,186 2,223,593 6,670,780 3,335,390 1,667,695 5,003,086 2,501,543 7,504,630 3,752,315 11,256,946 5,628,473 16,885,420 8,442,710 4,221,355 12,664,066 6,332,033 18,996,100 9,498,050 4,749,025 14,247,076 7,123,538 3,561,769 10,685,308 5,342,654 2,671,327 8,013,982 4,006,991 12,020,974 6,010,487 18,031,462 9,015,731 27,047,194 13,523,597 40,570,792 20,285,396 10,142,698 5,071,349 15,214,048 7,607,024 3,803,512 1,901,756 950,878 475,439 1,426,318 713,159 2,139,478 1,069,739 3,209,218 1,604,609 4,813,828 2,406,914 1,203,457 3,610,372 1,805,186 902,593 2,707,780

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