[seqfan] Re: Prime partitionalbe numbers and {P1} and {P2}

[Richard J. Mathar]

In sequel to http://list.seqfan.eu/pipermail/seqfan/2014-July/013301.html
and http://list.seqfan.eu/pipermail/seqfan/2014-June/013267.html :

If the sets {P1} and {P2} are (associated with) a prime partition of n,
then for every n=p1+p2 the p1 and p2 are in the same set, either P1 or P2.
This is obvious. If p1 and p2 were in different sets, then for
exactly one of the two  compositions
   n=p1+p2
or for
   n=p2+p1
the pair {p1,p2} would not find a (gcd(p1,P1) , gcd(p2,P2) ) <> (1,1),
because p1 would be a member of P2 and p2 a member of P1.

See A059756.