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Can-you-remember-this-formula-and-the-question-behind-it-mn-i-1-m-j-1-n-sign-gcd-i-j-1-The-first-prize-goes-to-that-one-who-can-tell-the-of-the-initial-question-




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.
$${Can}\:{you}\:{remember}\:{this}\:{formula}\:{and} \\ $$$${the}\:{question}\:{behind}\:{it}? \\ $$$$\:\:\:\:\boldsymbol{\Phi}=\boldsymbol{{mn}}−\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{m}}} {\boldsymbol{\sum}}}\:\underset{\boldsymbol{{j}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\:\boldsymbol{{sign}}\left[\boldsymbol{{gcd}}\left(\boldsymbol{{i}},\boldsymbol{{j}}\right)−\mathrm{1}\right] \\ $$$${The}\:{first}\:{prize}\:{goes}\:{to}\:{that}\:{one}\:{who} \\ $$$${can}\:{tell}\:{the}\:#\:{of}\:{the}\:{initial}\:{question}. \\ $$
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 Q12883.
$${This}\:{is}\:{a}\:{call}\:{for}\:{Filup}\:{Smith}\:{sir}\:{who} \\ $$$${was}\:{an}\:{active}\:{member}\:{in}\:{this}\:{forum} \\ $$$${for}\:{a}\:{long}\:{time}.\:{But}\:{sadly}\:{he}\:{seems}\:{to} \\ $$$${have}\:{left}\:{here}.\:{He}\:{is}\:{the}\:{one}\:{who}\:{asked} \\ $$$${the}\:{question}\:{behind}\:{this}\:{formula}.\:{You} \\ $$$${may}\:{find}\:{it}\:{in}\:{Q}\mathrm{12883}. \\ $$

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