There has to be a level of personal/private intent for this to be true.
I would argue that under a centrally planned economy, you could have the same number of people working, using the same tech/equipments and energy, but not be a good economy because the output isn't what those individual participants in the economy wants to consume.
and you've also casually mentioned 'useful', without saying to whom.
Basically, i am arguing that for productivity to be 'useful', it must be privately useful. Therefore, an economy must be producing something that an individual decided they want, rather than something that is commanded by an authority (such as a top-down command economy).
After all, the gov't authority might consider it useful to have holes dug by shovel, in order to occupy people and prevent them from doing other things.
I would argue that under a centrally planned economy, you could have the same number of people working, using the same tech/equipments and energy, but not be a good economy because the output isn't what those individual participants in the economy wants to consume.