Question Number 38812 by MrW3 last updated on 30/Jun/18
![Can you remember this formula and the question behind it? 𝚽=mn−𝚺_(i=1) ^m 𝚺_(j=1) ^n sign[gcd(i,j)−1] The first prize goes to that one who can tell the # of the initial question.](Q38812.png)
$${Can}\:{you}\:{remember}\:{this}\:{formula}\:{and} \\ $$$${the}\:{question}\:{behind}\:{it}? \\ $$$$\:\:\:\:\boldsymbol{\Phi}=\boldsymbol{{mn}}−\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{m}}} {\boldsymbol{\sum}}}\:\underset{\boldsymbol{{j}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\:\boldsymbol{{sign}}\left[\boldsymbol{{gcd}}\left(\boldsymbol{{i}},\boldsymbol{{j}}\right)−\mathrm{1}\right] \\ $$$${The}\:{first}\:{prize}\:{goes}\:{to}\:{that}\:{one}\:{who} \\ $$$${can}\:{tell}\:{the}\:#\:{of}\:{the}\:{initial}\:{question}. \\ $$
Commented by MrW3 last updated on 01/Jul/18
$${This}\:{is}\:{a}\:{call}\:{for}\:{Filup}\:{Smith}\:{sir}\:{who} \\ $$$${was}\:{an}\:{active}\:{member}\:{in}\:{this}\:{forum} \\ $$$${for}\:{a}\:{long}\:{time}.\:{But}\:{sadly}\:{he}\:{seems}\:{to} \\ $$$${have}\:{left}\:{here}.\:{He}\:{is}\:{the}\:{one}\:{who}\:{asked} \\ $$$${the}\:{question}\:{behind}\:{this}\:{formula}.\:{You} \\ $$$${may}\:{find}\:{it}\:{in}\:{Q}\mathrm{12883}. \\ $$