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A274605 Numbers n such that there is no prime between the n-th perfect power and the (n+1)-st perfect power. 1
3, 6, 8, 14, 60, 72, 216, 328, 361, 23268 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The perfect powers are given in A001597.

Numbers n such that A080769(n-1) = 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, Redmond-Sun 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 Fröhlich, Jun 30 2016

STATUS

approved

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Last modified February 26 02:19 EST 2020. Contains 332270 sequences. (Running on oeis4.)