OFFSET
1,1
COMMENTS
This property for prime p-1 = cube only numbers does not hold since the sum of 2 cubes has factors and p-1 = q^3 => p = q^3+1 = sum of 2 cubes.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
EXAMPLE
101 is included because 100 = 2^2*5^2 only square factors. 109 is not because while 108=2^2*3^3 has a square only factor it also has a cube factor.
MATHEMATICA
Select[Table[Prime[n], {n, 70000}], Length[Union[Last/@FactorInteger[#-1]]]==1&&Union[Last/@FactorInteger[#-1]]=={2}&] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)
PROG
(PARI) /* Input number of iterations n, power p and number to subtract k. */ powerfreep3(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(!ispowerfree3(x-k, p), c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) } ispowerfree3(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] == p1, flag=0, flag=1; break); ); return(flag) } /* this should be cleaned up, Joerg Arndt, Apr 09 2011 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 08 2003
STATUS
approved