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Results tagged with nt.number-theory
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user 106114
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
8
votes
Does this multiplicative function have a name? If so, what is known about it?
This is also called the Dedekind $\psi$ function:
$$
\psi(n):=n\prod_{p|n}(1+p^{-1})
$$
See also A001615 and A158523.
10
votes
A special type of generating function for Fibonacci
Perhaps interesting to note the following.
In the notation of Henri Cohen,
$$
F(x)=1 + x+\frac{x^2}{\color{red} 2}-\frac{x^3}{\color{red} 3}+\frac{x^4}{\color{red}8}+\frac{x^5}{15}-\frac{25 x^6}{\col …