

A274605


Numbers n such that there is no prime between the nth perfect power and the (n+1)st perfect power.


1




OFFSET

1,1


COMMENTS

The perfect powers are given in A001597.
Numbers n such that A080769(n1) = 0.
Index of A116086(n) in A001597.
Numbers n such that A000720(A001597(n)) = A000720(A001597(n+1)).
It has been conjectured that 23268 is the last term of the sequence.


LINKS

Table of n, a(n) for n=1..10.
Wikipedia, RedmondSun conjecture.


EXAMPLE

25 is the 6th perfect power, i.e., 25 = A001597(6), and there is no prime between 25 and the next larger perfect power A001597(7) = 27, so 25 is a term of A116086, and thus 6 is a term of this sequence.


MATHEMATICA

Position[Count[#, _?PrimeQ] & /@ Range @@@ # &@ Partition[#, 2, 1] &@ Select[Range[10^5], # == 1  GCD @@ FactorInteger[#][[All, 2]] > 1 &], 0] // Flatten (* Michael De Vlieger, Jun 30 2016 *)


PROG

(PARI) a001597(n) = my(i=0, k=0); while(1, if(ispower(k)  k==1, i++); if(i==n, return(k)); k++)
a080769(n) = primepi(a001597(n+1))primepi(a001597(n))
is(n) = a080769(n)==0


CROSSREFS

Cf. A001597, A080769, A116086.
Sequence in context: A108161 A263349 A297211 * A213983 A174133 A261928
Adjacent sequences: A274602 A274603 A274604 * A274606 A274607 A274608


KEYWORD

nonn


AUTHOR

Felix FrÃ¶hlich, Jun 30 2016


STATUS

approved



