2023.11.6 闲话

如果知道行、列的 EGF 求后缀是否能简单做呢？

我咋能知道第二类斯特林数 BGF。。

1-2-3=-4。

BM 时代，沸腾期待！

Children of the Machine - Dagames, CG5

I'll show you the truth
I'll show you your purpose
Just a pencil and a dream
Created for entertainment
He lives on, through us
Born from darkness, born from lust
Cause when, we reach the end, we do it all over again

Follow me, we're children of the machine
Barely human in a city built of broken dreams
Follow me, we're children of the machine
Barely human in a city built of broken dreams

It's a joyless job
When you heart's running empty at the seams (the seams)
But after eons filling up the bottle
Singing on a desperate pencil and a dream
Well, the void was filled when you lived
To the empty ink, then we would sink
To the beat of a cog wheel turning
Love was the fuel that kept me from burning
To create this finest design
You need a magic darker than mine
And a kiss from the angels
Casting demons down the bottom line!

So wonderful how deep the love can flow
'Cause when you came into my life
I couldn't bear to let go
But the curtain came to a close

He lives on through us
We're born from darkness, born from lust
'Cause when we reach the end
We do it all over again

Follow me, we're children of the machine (we've built this machine)
Barely a human in a city built of broken dreams (ohh-oh)
Follow me, we're children of the machine (you came to life)
Barely a human in a city built of broken dreams

In the dark nightmares, see the spotlight glare
And accept your fate in time (and time)
In the dark nightmares, see the spotlight glare
And accept your fate in time

Follow me, we're children of the machine (ahh-ah)
Barely a human in a city built of broken dreams

我给 OI 微氪 20 多 w，一千多天活跃天数，数论探索 50% 数数 10% DP 5%。全算法收集，只有几个零熟练的三四熟练的，很多都满熟练了。

出比赛必打除 NOIP 嫖来的。CCF 的读物、证书我都买了，我每天早晨都会听 CCF 的宣传片。

CCF 官方出的大纲一个不落全买了。CCF 抽奖必转发，咕值活动必参加，周边证书必买、独立命题联动我把城里的全买了遍，剩下做不完的给了学弟。

CCF 我把随随便便白嫖来的咕值换了很多 OI 的周边，不得不说 CCF 大人福利满满。

我家里有很多 OI 家具，客厅摆着 NOI 系列比赛数据和 NOI 吉祥物。餐桌上放着一个 NOI 吉祥物，我屋里摆一个，爸妈屋里摆一个，门口摆一个，厨房摆一个，阳台摆一个，厕所就不摆了我怕玷污信宝。我床上还有两个公仔。

我文具袋上书包上都挂着算法的吊饰，我最喜欢的是 CRT，因为他象征我们的文化底蕴。

我是个重度老二次元，最喜欢的动漫是 JOJO 的奇妙冒险、刀剑神域、关于我转生成史莱姆这档事、国王排名、我的青春恋爱物语果然有问题、夏洛特、那年那兔那些事、回复术士的重启人生、世界顶尖的暗杀者，转生为异世界贵族、进击的巨人。

我反感学机器人和 whk 的，但我不会说他们不好，毕竟人各有好，有的人就是喜欢垃圾。

我不喜欢粪坑贴吧微博女拳那些素质低的平台，我经常逛洛谷的论坛和哔哩哔哩，OIer 素质才高。

我最瞧不起的是 MO 选手和 ChO 选手，但我看 B 友们说 ChO 选手感染新冠死了不知道是不是真的ĕ

ChO 水军你们好自为之，我不愿意跟你们吵架。

我就是 CCF 程序设计能力 5 级萌新信卫兵，我给 CCF 当孝子怎么了？

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福利题

给定正整数 \(n\)，求：

\[\sum_{x=1}^n\sum_{x=1}^n\sum_{y=1}^n\mathop{\large\rm lcm}\limits_{\text{sym}}\dfrac{\operatorname{lcm}(x,z)\cdot\gcd(y,z)}{\gcd(x,y)} \]

问题的关键在于计算 \(f(x,y,z)=\mathop{\large\rm lcm}\limits_{\text{sym}}\dfrac{\operatorname{lcm}(x,z)\cdot\gcd(y,z)}{\gcd(x,y)}\) .

对于每个素因子分别考虑：

\[\begin{aligned}f(x,y,z)&=\prod_{p\in\mathbb P}\max_{\text{sym}}p^{\max\{v_p(x),v_p(z)\}+\min\{v_p(y),v_p(z)\}-\min\{v_p(x),v_p(y)\}}\\&=\prod_{p\in\mathbb P}p^{v_p(x)+v_p(y)+v_p(z)-2\min\{v_p(x),v_p(y),v_p(z)\}}\\&=\dfrac{x\cdot y\cdot z}{\gcd(x,y,z)^2}\end{aligned} \]

（注：第二个等号：仔细地讨论）

接下来就是莫反的工作了，平凡不述 .

类似地，也可以得到：

\[\mathop{\large\rm lcm}\limits_{\text{sym}}\dfrac{\operatorname{lcm}(x_1,x_k)\prod_{i=1}^{k-2}\gcd(x_{i},x_{i+1})}{\gcd(x_{k-1},x_k)}=\dfrac{\prod x_i}{(\gcd x_i)^2} \]

关于别的，次大公因数啥的可能需要讨论一下，太阴间了 .

可能这个题主要的意义是鱼鱼女装照 /se