数学 – 整数 - 2つの整数論的関数(Euilerの関数, Möbiusの関数)

代数系入門
(岩波書店)
松坂 和夫 (著)

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代数系入門 (松坂 和夫(著)、岩波書店)の第1章(整数)、8(2つの整数論的関数)、問1.を解いてみる。

問1.

$n,\phi \left(n\right),\mu \left(n\right)$
$\begin{array}{l}1,1,1\\ 2,1,-1\\ 3,2,-1\\ 4=2^2,2,0\\ 5,4,-1\\ 6=2·3,2,1\\ 7,6,-1\\ 8=2^3,4,0\\ 9=3^2,6,0\\ 10=2·5,4,0\\ 11,10,-1\\ 12=2^2·3,4,0\\ 13,12,-1\\ 14=2·7,6,1\\ 15=3·5,8,1\\ 16=2^4,8,0\\ 17,16,-1\\ 18=2·3^2,9,0\\ 19,18,-1\\ 20=2^2·5,8,0\\ 21=3·7,12,1\\ 22=2·11,10,1\\ 23,22,-1\\ 24=2^3·3,8,0\\ 25=5^2,20,0\\ 26=2·13,12,1\\ 27=3^3,18,0\\ 28=2^2·7,12,0\\ 29,28,-1\\ 30=2·3·5,8,-1\\ 31,30,-1\\ 32=2^5,16,0\\ 33=3·11,20,1\\ 34=2·17,16,1\\ 35=5·7,24,1\\ 36=2^2·3^2,12,0\\ 37,36,-1\\ 38=2·19,18,1\\ 39=3·13,24,1\\ 40=2^3·5,16,0\\ 41,40,-1\\ 42=2·3·7,12,-1\\ 43,42,-1\\ 44=4·11,20,1\\ 45=3^2·5,30,0\\ 46=2·23,22,1\\ 47,46,-1\\ 48=2^4·3,16,0\\ 49=7^2,42,0\\ 50=2·5^2,20,0\end{array}$
$\begin{array}{l}51=3·17,32,1\\ 52=2^2·13,24,0\\ 53,52,-1\\ 54=2·3^3,18,0\\ 55=5·11,40,1\\ 56=2^3·7,24,0\\ 57=3·19,36,1\\ 58=2·29,28,1\\ 59,58,-1\\ 60=2^2·3·5,16,0\\ 61,60,-1\\ 62=2·31,30,1\\ 63=3^2·7,36,0\\ 64=2^6,32,0\\ 65=5·13,48,1\\ 66=2·3·11,20,-1\\ 67,66,-1\\ 68=2^2·17,32,0\\ 69=3·13,24,1\\ 70=2·5·7,24,-1\\ 71,70,-1\\ 72=2^3·3^2,24,0\\ 73,72,-1\\ 74=2·37,36,1\\ 75=5^3,60,0\\ 76=2^2·19,18,0\\ 77=7·11,60,1\\ 78=2·3·13,24,-1\\ 79,78,-1\\ 80=2^4·5,32,0\\ 81=3^4,54,0\\ 82=2·41,40,1\\ 83,82,-1\\ 84=2^2·3·7,24,0\\ 85=5·17,64,1\\ 86=2·43,42,1\\ 87=3·29,56,1\\ 88=2^3·11,40,0\\ 89,88,-1\\ 90=2·3^2·5,30,0\\ 91=7·13,72,1\\ 92=2^2·23,44,0\\ 93=3·31,60,1\\ 94=2·47,46,1\\ 95=5·19,72,1\\ 96=2^5·3,32,0\\ 97,96,-1\\ 98=2·7^2,42,0\\ 99=3^2·11,60,0\\ 100=2^2·5^2,40,0\end{array}$