1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
|
\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input INTHEORY.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
<<*>>=
-- Input generated from IntegerNumberTheoryFunctionsXmpPage
)clear all
div144 := divisors(144)
#(div144)
reduce(+,div144)
numberOfDivisors(144)
sumOfDivisors(144)
f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])
f1(200)
f1(846)
f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])
f2(200)
f2(846)
fibonacci(25)
[fibonacci(n) for n in 1..15]
fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])
fib(25)
[fib(n) for n in 1..15]
legendre(3,5)
legendre(23,691)
h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))
h(-163)
h(-499)
h(-1832)
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
