2024.3.27 闲话
歌:もうまい - suni feat. 初音ミク .
因为 APJ 有歌词所以发一篇 .
CG5 - HIGH
Okay okay oka-a-ay okay oh
Okay okay okay okay oh
Okay okay oka-a-ay okay oh
Okay okay okay okay oh
You've been on my mind
So meet my melody in the relative major
Flows so well
Like you and me
Goes to the beat
We're so perfect on paper
Think the stars have aligned
I'll tell you why
But they've aligned in our favor
'Cause we just get along
So-o-o can we just get along
La la la la
Take me high what I say
And she takes me high
High
Take me high what I say
And she takes me higher oh oh
Take me high that's what I said
Won't you take me high
High
A little bit of lovin' won't do
Give me all of you now
This is a story I'ma tell right now
Of a life of singularity a life so foul
This man he ran away from love what
Too meticulous particular and never enough
One of the stranger things when you're upside down
In a gauntlet where your thoughts been knockin' you around
It's confliction hey commotion hey confusion hey corruption
Don't wanna suffer the repercussions of a commitment concussion ho
He continued on with caution
A connection crusade
What
But she got through the armor
Cut through with a blade of what
Caring compassion and kindness too
And his only defense was I love you ho
Take me high what I say
And she takes me high hey yeah
Take me higher
Take me high what I say
And she takes me higher
Yeah yeah yeah
Take me high that's what I said
Won't you take me high high
A little bit of lovin' won't do
Give me all of you
Give me ya give me ya
Take me high what I say
And she takes me high hey yeah
Take me higher
Take me high what I say
And she takes me higher
Take me high that's what I said
Won't you take me high
Don't take me down
A little bit of lovin' won't do
Give me all of you
Take me high take me higher
估计:
解答:
令 \(g_k(n)\) 是 \(\{1,2,\cdots,n\}\) 中 GCD 为 1 的 \(k\) 元子集个数,则:
从而:
也即:
然而这又有什么用呢?
注意到 \(f_k(n)\) 即为 \(\{1,2,\cdots,n\}\) 中 GCD 与 \(n\) 互质的 \(k\) 元子集数量,于是:
从而和 \(g_k\) 类似分析,展开前几项就可以得到:
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