cp's OEIS Frontend

A377433 Number of non-perfect-powers x in the range prime(n) < x < prime(n+1).

%I A377433 #8 Nov 04 2024 09:06:13
%S A377433 0,0,1,1,1,2,1,3,3,1,3,3,1,3,4,5,1,4,3,1,5,2,5,7,2,1,3,1,3,11,2,5,1,8,
%T A377433 1,5,5,3,4,5,1,9,1,2,1,11,10,2,1,3,5,1,8,4,5,5,1,5,3,1,8,13,3,1,3,12,
%U A377433 5,8,1,3,5,6,5,5,3,5,7,2,7,9,1,9,1,5,2
%N A377433 Number of non-perfect-powers x in the range prime(n) < x < prime(n+1).
%C A377433 Non-perfect-powers (A007916) are numbers without a proper integer root.
%C A377433 Positions of terms > 1 appear to be A049579.
%F A377433 a(n) + A377432(n) = A046933(n) = prime(n+1) - prime(n) - 1.
%e A377433 Between prime(4) = 7 and prime(5) = 11 the only non-perfect-power is 10, so a(4) = 1.
%t A377433 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A377433 Table[Length[Select[Range[Prime[n]+1, Prime[n+1]-1],radQ]],{n,100}]
%Y A377433 Positions of 1 are latter terms of A029707.
%Y A377433 Positions of terms > 1 appear to be A049579.
%Y A377433 For prime-powers instead of non-perfect-powers we have A080101.
%Y A377433 For non-prime-powers instead of non-perfect-powers we have A368748.
%Y A377433 Perfect-powers in the same range are counted by A377432.
%Y A377433 A000040 lists the primes, differences A001223.
%Y A377433 A000961 lists the powers of primes, differences A057820.
%Y A377433 A001597 lists the perfect-powers, differences A053289, seconds A376559.
%Y A377433 A007916 lists the non-perfect-powers, differences A375706.
%Y A377433 A065514 gives the greatest prime-power < prime(n), difference A377289.
%Y A377433 A081676 gives the greatest perfect-power <= n.
%Y A377433 A246655 lists the prime-powers not including 1, complement A361102.
%Y A377433 A366833 counts prime-powers between primes, see A053706, A053607, A304521, A377286.
%Y A377433 A377468 gives the least perfect-power > n.
%Y A377433 Cf. A000015, A002808, A024619, A031218, A064113, A065890, A244508, A377282, A377434, A377436, A377466, A377467.
%K A377433 nonn
%O A377433 1,6
%A A377433 _Gus Wiseman_, Nov 02 2024