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 A377431 #6 Oct 31 2024 11:22:44 %S A377431 3,4,6,8,9,10,11,12,13,14,15,16,18,19,21,22,23,24,26,27,29,30,31,32, %T A377431 33,34,36,37,38,39,40,42,44,46,47,48,50,51,53,54,55,56,58,59,60,61,62, %U A377431 63,65,66,67,68,71,72,73,74,75,76,77,78,79,80,82,84,85,86 %N A377431 Numbers k such that there is at least one squarefree number between prime(k)+1 and prime(k+1)-1. %e A377431 Primes 4 and 5 are 7 and 11, and the interval (8,9,10) contains 10, which is squarefree, so 4 is in the sequence. %t A377431 Select[Range[100], Length[Select[Range[Prime[#]+1,Prime[#+1]-1],SquareFreeQ]]>=1&] %Y A377431 These are the positive positions in A061398, or terms >= 2 in A373198. %Y A377431 The complement (no squarefree numbers) is A068360. %Y A377431 For prime-power instead of squarefree we have A377057, strict version A377287. %Y A377431 For exactly one squarefree number we have A377430. %Y A377431 A000040 lists the primes, differences A001223, seconds A036263. %Y A377431 A002808 lists the composites, complement A008578. %Y A377431 A005117 lists the squarefree numbers, complement A013929. %Y A377431 A377038 gives k-differences of squarefree numbers. %Y A377431 Cf. A007674, A013603, A029707, A036378, A046933, A072284, A076259, A077641, A077643, A075526, A078147, A112925, A112926, A120992, A293697. %K A377431 nonn %O A377431 1,1 %A A377431 _Gus Wiseman_, Oct 29 2024