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A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd. A sphenic number has Ω(n) = 3 ...
A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two ... d = 1, 3, 7, 9) are ... bases up to 1052) Padilla, Tony (7 ...
The sum of its factors (including one and itself) sum to 360, exactly three times 120. Perfect numbers are order two ( 2-perfect ) by the same definition. 120 is the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of two (8 + 16 + 32 + 64), and four consecutive powers ...
Two million dollars may seem like more than enough money for retirement, but even that amount can vanish quickly in the face of medical expenses, inflation and taxes. If you expect to retire at 50 ...
Saving $1 million (or more) for retirement is a great goal to have. Putting that much aside could make it easier to live your preferred lifestyle when you retire, without having to worry about ...
A viral post shared on Threads claims President-elect Donald Trump lost the popular vote by 2% in the 2024 election. View on Threads Verdict: False The claim is false. Multiple sources, including ...
The square-free number 42 has factorization 2 × 3 × 7, or as an infinite product 2 1 · 3 1 · 5 0 · 7 1 · 11 0 · 13 0 ··· Thus the number 42 may be encoded as the binary sequence ...001011 or 11 decimal. (The binary digits are reversed from the ordering in the infinite product.)
Prepare yourself for the possibility of an eight-way tie atop the SEC standings. It’s not even that hard to imagine. This is all it would take: First, No. 10 Georgia beats No. 4 Tennessee on ...