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12:14 AM
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Q: Are there no semiprimes of the form $n^n+n!$, where $n \gt 7$?

MathphileI searched for semiprimes of the form of $n^n+n!$, where $n \in \Bbb{N}$, for a range of $n \le 2 \times 10^4$ on PARI/GP and found semiprimes of the form $n^n+n!$ only for $n=2, 3, 7$. We can write $n^n+n!$ as: $$n^n+n!=n(n^{n-1}+(n-1)!)$$ Therefore we can also alternatively look for primes of ...

In mathematics, a semiprime is a natural number that is the product of two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes. == Examples and variations == The semiprimes less than 100 are: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, and 95 (sequence A001358 in the OEIS).Semiprimes that are not square numbers are...
 
 
8 hours later…
8:19 AM
3
Q: How to obtain the analytic representation of the given infinite series?

Asit SrivastavaThis series is given in Griffiths Introduction to Electrodynamics chapter 3 in an example explaining seperation of variables. $$V(x,y) = \frac{4V_0}{\pi} \sum_{n=1,3,5\ldots} \frac{1}{n}e^{-n\pi x/a}\sin(n\pi y/a)$$ $$V(x,y) = \frac{2V_0}{\pi} \tan^{-1}\left(\frac{\sin(\pi y/a)}{\sinh(\pi x...

 

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