A143813 Sum of two powerful numbers greater than 1.

8, 12, 13, 16, 17, 18, 20, 24, 25, 29, 31, 32, 33, 34, 35, 36, 40, 41, 43, 44, 45, 48, 50, 52, 53, 54, 57, 58, 59, 61, 63, 64, 65, 68, 72, 73, 74, 76, 80, 81, 85, 88, 89, 90, 91, 96, 97, 98, 99, 100, 104, 106, 108, 109, 112, 113, 116, 117, 121, 124, 125, 127

Offset: 1

Author

Charles R Greathouse IV, Jul 06 2011

Keywords

• nonn

Comments

A076871 is the primary sequence.

Examples

			8 = 4 + 4, 12 = 4 + 8, 13 = 4 + 9.
		

Programs

PARI

isP(n)={
  n>3 && vecmin(factor(n)[,2])>1
};
sumset(a,b)={
  my(c=vector(#a*#b));
  for(i=1,#a,
    for(j=1,#b,
      c[(i-1)*#b+j]=a[i]+b[j]
    )
  );
  vecsort(c,,8)
};
upto(lim)={
  my(v=select(isP, vector(floor(lim),i,i)));
  select(n->n<=lim, sumset(v,v))
};