This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378374 #5 Dec 18 2024 23:32:21
%S A378374 128,225,256,64009,1295044
%N A378374 Perfect powers p such that the interval from the previous perfect power to p contains a unique prime.
%C A378374 Also numbers appearing exactly once in A378249.
%F A378374 We have a(n) < A178700(n) < A378355(n).
%e A378374 The consecutive perfect powers 125 and 128 have interval (125, 126, 127, 128) with unique prime 127, so 128 is in the sequence.
%t A378374 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A378374 y=Table[NestWhile[#+1&,Prime[n],radQ[#]&],{n,1000}];
%t A378374 Select[Union[y],Count[y,#]==1&]
%Y A378374 The previous prime is A178700.
%Y A378374 For prime powers instead of perfect powers we have A345531, difference A377281.
%Y A378374 Opposite singletons in A378035 (union A378253), restriction of A081676.
%Y A378374 For squarefree numbers we have A378082, see A377430, A061398, A377431, A068360.
%Y A378374 Singletons in A378249 (run-lengths A378251), restriction of A377468 to the primes.
%Y A378374 If the same interval contains at least one prime we get A378250.
%Y A378374 For next instead of previous perfect power we have A378355.
%Y A378374 Swapping "prime" with "perfect power" gives A378364.
%Y A378374 A000040 lists the primes, differences A001223.
%Y A378374 A001597 lists the perfect powers, differences A053289.
%Y A378374 A007916 lists the non perfect powers, differences A375706.
%Y A378374 A069623 counts perfect powers <= n.
%Y A378374 A076411 counts perfect powers < n.
%Y A378374 A080769 counts primes between perfect powers.
%Y A378374 Cf. A023055, A045542, A052410, A216765, A376560, A377287, A378356.
%K A378374 nonn,more
%O A378374 1,1
%A A378374 _Gus Wiseman_, Dec 17 2024