OFFSET
1,3
COMMENTS
Besides first 1, all other terms are positive. At n>16, the function pp(n)-p(n) is (apparently) monotonically increasing.
EXAMPLE
pp(3)-p(3)= 8-5=3.
MATHEMATICA
Module[{upto=2000, pp, pr, len}, pp=Flatten[Table[Range[Surd[upto, n]]^n, {n, 2, Sqrt[ upto]}]]//Union; pr=Prime[Range[PrimePi[upto]]]; len=Min[ Length[ pp], Length[pr]]; #[[1]]-#[[2]]&/@Thread[ {Take[pp, len], Take[ pr, len]}]] (* Harvey P. Dale, Feb 23 2018 *)
PROG
(PARI) lista(nn) = {vec = vector(nn, i, i); pp = select(i->((ispower(i) || (i==1))), vec); for (i = 1, #pp, print1(pp[i] - prime(i), ", "); ); } \\ Michel Marcus, Oct 02 2013
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Zak Seidov, Oct 11 2002
STATUS
approved