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 A378355 #11 Feb 07 2025 21:32:17
%S A378355 125,216,243,64000,1295029,2535525316,542939080312
%N A378355 Numbers appearing exactly once in A378035 (greatest perfect power < prime(n)).
%C A378355 These are perfect-powers p such that the interval from p to the next perfect power contains a unique prime.
%C A378355 Is this sequence infinite? See A178700.
%F A378355 A151800(a(n)) = A178700(n).
%e A378355 We have 125 because 127 is the only prime between 125 and 128.
%t A378355 radQ[n_]:=n>1&&GCD@@Last/@FactorInteger[n]==1;
%t A378355 y=Table[NestWhile[#-1&,Prime[n],radQ[#]&],{n,1000}];
%t A378355 Select[Union[y],Count[y,#]==1&]
%Y A378355 The next prime is A178700.
%Y A378355 Singletons in A378035 (union A378253), restriction of A081676.
%Y A378355 The next perfect power is A378374.
%Y A378355 Swapping primes and perfect powers gives A379154, unique case of A377283.
%Y A378355 A000040 lists the primes, differences A001223.
%Y A378355 A001597 lists the perfect powers, differences A053289.
%Y A378355 A007916 lists the not perfect powers, differences A375706.
%Y A378355 A069623 counts perfect powers <= n.
%Y A378355 A076411 counts perfect powers < n.
%Y A378355 A377432 counts perfect powers between primes, see A377434, A377436, A377466.
%Y A378355 A378249 gives least perfect power > prime(n) (run-lengths A378251), restrict of A377468.
%Y A378355 Cf. A000961, A031218, A045542, A052410, A067871, A076412, A080769, A131605, A188951, A216765, A378250, A378356.
%K A378355 nonn,more
%O A378355 1,1
%A A378355 _Gus Wiseman_, Nov 26 2024