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A143813 Sum of two powerful numbers greater than 1.

%I A143813 #13 Sep 25 2012 16:19:04
%S A143813 8,12,13,16,17,18,20,24,25,29,31,32,33,34,35,36,40,41,43,44,45,48,50,
%T A143813 52,53,54,57,58,59,61,63,64,65,68,72,73,74,76,80,81,85,88,89,90,91,96,
%U A143813 97,98,99,100,104,106,108,109,112,113,116,117,121,124,125,127
%N A143813 Sum of two powerful numbers greater than 1.
%C A143813 A076871 is the primary sequence.
%e A143813 8 = 4 + 4, 12 = 4 + 8, 13 = 4 + 9.
%o A143813 (PARI) isP(n)={
%o A143813   n>3 && vecmin(factor(n)[,2])>1
%o A143813 };
%o A143813 sumset(a,b)={
%o A143813   my(c=vector(#a*#b));
%o A143813   for(i=1,#a,
%o A143813     for(j=1,#b,
%o A143813       c[(i-1)*#b+j]=a[i]+b[j]
%o A143813     )
%o A143813   );
%o A143813   vecsort(c,,8)
%o A143813 };
%o A143813 upto(lim)={
%o A143813   my(v=select(isP, vector(floor(lim),i,i)));
%o A143813   select(n->n<=lim, sumset(v,v))
%o A143813 };
%K A143813 nonn
%O A143813 1,1
%A A143813 _Charles R Greathouse IV_, Jul 06 2011