I think there was a formula for that by Michele Ferrari but I can't find it on the net. I think it can't be bigger than around 6,5 watt per kg for at least an hour or so. Does anybody know the exact number and how it is calculated?
Wilson, in Bicycling Science has a plot that's not quite what you're looking for but very close. Closer than it looks at first, I believe.
click for full size
The downside of this is that it isn't normalised to bodyweight. But there are significant error margins - small in the case of ergometer test, but much larger in the case of things like Indurain's TdF climb or even Boardman's hour record. Large enough, I would say, that we can use and average bodyweight. Even between pros, W/kg will vary. Even for a given rider there will be day-to-day variations.
Apparently the average pro cyclist weighs 68kg, so we can get a pretty decent value by dividing that out, or find a specific riders' weight. Taking Boardman's 1996 hour record as an example, that reads off as 420W (give or take about 10W). He's supposed to weigh 70kg (I don't know when that figure applies to) giving 6 W/kg.
To answer the question with a value representative of peak professional performance instead of naming a specific human, I think this precision is probably sensible.
I think the answers so far are slightly underestimating maximal w/kg FTPs. I've included a table showing FTPs (and maximal powers recorded for shorter periods of time) from the following site. In the table you can see that for men the maximal W/kg FTP is a fair bit over 6 w/kg when fresh.
As an aside, hour record attempts probably won't be the best sources for maximal W/kg since they don't involve climbing and performance instead depends on total watts produced (or more accurately W/CdA). Larger riders tend to have higher FTPs in total watts (and often W/CdA though some small riders can get a really low CdA) while smaller riders tend to have higher W/kg.
Michele Ferrari, the infamous doping doctor for Lance Armstrong and a number of other riders, did make a related statement. In Tyler Hamilton's autobiography, Hamilton reported that Ferrari said the following (around the year 2000, also this is his paraphrase of Ferrari, not a verbatim quote)
He explained that the best measure of ability was in watts per kilogram—the amount of power you produce, divided by your weight. He said that 6.7 watts per kilogram was the magic number, because that was what it took to win the Tour.
However, I'm not sure what duration that figure refers to. The preceding page says that Ferrari often tested athletes on the Col de la Madone, for which the current men's KOM is held by Richie Porte at 34 minutes 43 seconds. Ferrari could have been referring to functional threshold power over 6.7 W/kg. Commonly, people understand FTP to be the power you can hold for about one hour - however, time to exhaustion at FTP varies, and my understanding is that it's commonly around 30-75 minutes, depending on the person. If Ferrari meant completing the Madone with an average over 6.7 W/kg, that's different. There are models that would enable you to estimate someone's FTP given their power at shorter durations (the critical power model needs at least 2 data points; critical power is generally close to FTP). I have not run these models, but I bet you that this performance still implies an FTP at least 6.4 W/kg. Also remember that this is the doping era, so presumably all contenders were on EPO and other drugs.
In any case, Ferrari did not state how much power a human "can sustain", which sort of implies the physics-based upper limit to the cycling power we can generate.
Continuing with the thread of power to weight ratios in the doping era, Ross Tucker reports here that Bjarne Riis is estimated to have sustained 6.8 W/kg up the Hautacam in 1996, and Lance Armstrong is estimated to have done 6.6 W/kg up the Alpe d'Huez. The Strava segments for each climb are linked. Note that here, weight was presumably based off reported data (which might be incorrectly reported, since athletes don't typically make their weights public), and estimated power data. They weren't racing with any power meters then. The SRM was the only available power meter, and it was very bulky and heavy. There is a wide error margin around those estimates. Note that these are climbs at the end of a long race, but the leaders would have been protected by their teams and they probably at least had time to recover before the last climb.
Later in the post, Tucker said that
I am of the opinion, like Prof Aldo Sassi, that a value above 6.2 W/kg is indicative of doping.
He didn't clearly say what "a value" refers to. Going to the previous paragraphs, he was talking about Armstrong producing the estimated power at 85-90% of his VO2max. I don't know how that output relates to threshold power. I would guess it's around threshold, maybe plus or minus 2-3%. Either way, it's something you can sustain for a while but not the whole day.
It's worth remembering that this post was made in 2010. We have continued to make advancements in training since then. For example, technology means that indoor training is now much more prevalent and accessible, which aids in structured training, maintenance of form over the winter, and also talent discovery. If you are estimating power from assumptions (e.g. estimate the power a rider would need to complete an ascent given assumptions about their weight, the wind, etc), bikes have become more aero, which may mean that they hit the final climbs fresher. Nutrition has improved. For example, riders now target very high carb intakes to ensure a constant glycogen supply to the muscles. All of this may mean that the ceiling on clean W/kg has grown.
Teams may also have paid more attention to managing rider weight, which is the denominator in W/kg. This can be fine, but it can also be ethically problematic. It might breed eating disorders and relative energy deficiency in sport (RED-S), which women may be more vulnerable to but which men can also experience. Team Sky was suspected to be pushing the rules on corticosteroid therapeutic use exemptions in the early 2010s. If true, one of their reasons may have been to help athletes manage weight from muscle catabolism (although in the short term, they can also cause water retention).
Of note, MyWindSock estimated that Vingegaard did about 7.6 W/kg for 13 mins, 21 secs, up the climb in the stage 16 TT of the 2023 Tour de France. Zach Nehr, writing for Velo (then Velonews) has also produced some estimates up significant climbs in the 2023 Tour. Notably, he thinks that Pogačar and Vingegaard did about 6.1 W/kg up the Alpe d'Huez (nearly 40 minute climb). Sepp Kuss had a maximum 20 minute power of 6.3 W/kg; note that taking 95% of a 20 minute effort can be used to estimate a rider's threshold outside of an FTP test, but that estimate is likely to be biased one way or another.
The book citation is: Hamilton, Tyler; Coyle, Daniel. (The Secret Race: Inside the Hidden World of the Tour de France . Random House Publishing Group. Kindle Edition.