Merci! Il y en a d’autres effectivement: 30,31,32,37,43,50,55…

]]>Here is the simple way I found to generate noble integers < or = to 60.

Start with 1/2 + 1/2 =1

Now use the equality 1/m=[1/(m+1)]+[1/m(m+1)] and apply it to 1/2

You get 1/2 + 1/3 + 1/6 =1 and n=2+3+6=11

In 1/2 + 1/3 + 1/6 replace 1/3 by 1/4 + 1/12 so that you get 1/2 + 1/4 + 1/6 +1/12 =1

and n=2+4+6+12=24

In 1/2 + 1/3 + 1/6 replace 1/6 by 1/7 + 1/42 so that you get 1/2 + 1/3 + 1/7 +1/42 =1

and n=2+3+7+42=54

In 1/2 + 1/4 + 1/6 +1/12 replace 1/4 by 1/5 by 1/20 so that you get 1/2 + 1/5 + 1/6 +1/12 + 1/20=1

and n=2+5+6+12+20=45

But, I do not know if this is an exhaustive list of these numbers.

JL Foulley

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