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 A075146 n-th perfect power - n-th prime: pp(n) - prime(n). 0
 -1, 1, 3, 2, 5, 12, 10, 13, 13, 20, 33, 44, 59, 78, 78, 75, 85, 108, 129, 145, 152, 164, 173, 200, 227, 242, 258, 293, 332, 371, 385, 398, 439, 486, 527, 578, 627, 678, 733, 788, 821, 843, 898, 963, 1028, 1097, 1120, 1146, 1217, 1292, 1367, 1442, 1487, 1513, 1592 (list; graph; refs; listen; history; text; internal format)
 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. LINKS FORMULA a(n) = A001597(n) - A000040(n). 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 Cf. A001597. Sequence in context: A305878 A093924 A130597 * A300939 A062941 A211018 Adjacent sequences:  A075143 A075144 A075145 * A075147 A075148 A075149 KEYWORD easy,sign AUTHOR Zak Seidov, Oct 11 2002 STATUS approved

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Last modified October 30 03:24 EDT 2020. Contains 338076 sequences. (Running on oeis4.)