cp's OEIS Frontend

A377436 Numbers k such that there is no perfect-power x in the range prime(k) < x < prime(k+1).

%I A377436 #6 Nov 04 2024 09:15:48
%S A377436 1,3,5,7,8,10,12,13,14,16,17,19,20,21,23,24,26,27,28,29,32,33,35,36,
%T A377436 37,38,40,41,42,43,45,46,49,50,51,52,55,56,57,58,59,60,62,63,64,65,67,
%U A377436 69,70,71,73,74,75,76,77,79,80,81,82,83,84,86,87,88,89,90
%N A377436 Numbers k such that there is no perfect-power x in the range prime(k) < x < prime(k+1).
%C A377436 Perfect-powers (A001597) are numbers with a proper integer root, complement A007916.
%e A377436 Primes 8 and 9 are 19 and 23, and the interval (20,21,22) contains no prime-powers, so 8 is in the sequence.
%t A377436 perpowQ[n_]:=n==1||GCD@@FactorInteger[n][[All,2]]>1;
%t A377436 Select[Range[100],Length[Select[Range[Prime[#]+1, Prime[#+1]-1],perpowQ]]==0&]
%Y A377436 For powers of 2 instead of primes see A377467, A013597, A014210, A014234, A244508.
%Y A377436 For squarefree instead of perfect-power we have A068360, see A061398, A377430, A377431.
%Y A377436 For just squares (instead of all perfect-powers) we have A221056, primes A224363.
%Y A377436 For prime-powers (instead of perfect-powers) we have A377286.
%Y A377436 These are the positions of 0 in A377432.
%Y A377436 For one instead of none we have A377434, for prime-powers A377287.
%Y A377436 For two instead of none we have A377466, for prime-powers A377288, primes A053706.
%Y A377436 A000015 gives the least prime-power >= n.
%Y A377436 A000040 lists the primes, differences A001223.
%Y A377436 A000961 lists the powers of primes, differences A057820.
%Y A377436 A046933 counts the interval from A008864(n) to A006093(n+1).
%Y A377436 A065514 gives the nearest prime-power before prime(n)-1, difference A377289.
%Y A377436 A080101 and A366833 count prime-powers between primes, see A377057, A053607, A304521.
%Y A377436 A081676 gives the nearest perfect-power up to n.
%Y A377436 A246655 lists the prime-powers not including 1, complement A361102.
%Y A377436 A377468 gives the nearest perfect-power after n.
%Y A377436 Cf. A001597, A002808, A024619, A053707, A064113, A065890, A075526, A276781, A345531, A376597, A377054, A377282.
%K A377436 nonn
%O A377436 1,2
%A A377436 _Gus Wiseman_, Nov 02 2024