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 A376592 #6 Oct 05 2024 09:40:53 %S A376592 2,3,5,6,7,8,10,13,15,17,19,20,22,23,25,26,28,29,30,31,34,36,37,38,39, %T A376592 41,42,44,45,46,47,49,50,51,52,54,57,59,60,61,63,64,66,67,69,70,72,73, %U A376592 74,75,76,77,78,80,81,82,83,85,86,88,89,90,91,92,93,94,95 %N A376592 Points of nonzero curvature in the sequence of squarefree numbers (A005117). %C A376592 These are points at which the second differences (A376590) are nonzero. %H A376592 Gus Wiseman, <a href="/A376592/a376592.png">Points of nonzero curvature in the squarefree numbers</a>. %e A376592 The squarefree numbers (A005117) are: %e A376592 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, ... %e A376592 with first differences (A076259): %e A376592 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, ... %e A376592 with first differences (A376590): %e A376592 0, 1, -1, 0, 2, -2, 1, -1, 0, 1, 0, 0, -1, 0, 2, 0, -2, 0, 1, -1, 0, 1, -1, 0, 1, ... %e A376592 with nonzeros at (A376591): %e A376592 2, 3, 5, 6, 7, 8, 10, 13, 15, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 34, 36, ... %t A376592 Join@@Position[Sign[Differences[Select[Range[100], SquareFreeQ],2]],1|-1] %Y A376592 The first differences were A076259, see also A375927, A376305, A376306, A376307, A376311. %Y A376592 These are the nonzeros of A376590. %Y A376592 The complement is A376591. %Y A376592 A000040 lists the prime numbers, differences A001223. %Y A376592 A005117 lists squarefree numbers, complement A013929 (differences A078147). %Y A376592 A073576 counts integer partitions into squarefree numbers, factorizations A050320. %Y A376592 For points of nonzero curvature: A333214 (prime), A376603 (composite), A376589 (non-perfect-power), A376595 (nonsquarefree), A376598 (prime-power), A376601 (non-prime-power). %Y A376592 For squarefree numbers: A076259 (first differences), A376590 (second differences), A376591 (inflection and undulation points). %Y A376592 Cf. A007674, A036263, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A333254, A373198, A376655. %K A376592 nonn %O A376592 1,1 %A A376592 _Gus Wiseman_, Oct 04 2024