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 A376595 #5 Oct 05 2024 09:40:32 %S A376595 1,2,3,4,6,7,8,9,10,14,15,16,18,21,22,23,24,26,27,28,29,30,31,32,34, %T A376595 35,36,38,42,43,44,45,46,48,49,50,51,52,54,55,56,58,59,60,61,63,64,65, %U A376595 66,67,68,69,72,73,74,75,77,78,79,80,84,85,86,87,89,90,91 %N A376595 Points of nonzero curvature in the sequence of nonsquarefree numbers (A013929). %C A376595 These are points at which the second differences (A376593) are nonzero. %H A376595 Gus Wiseman, <a href="/A376595/a376595.png">Points of nonzero curvature in the nonsquarefree numbers</a>. %e A376595 The nonsquarefree numbers (A013929) are: %e A376595 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, ... %e A376595 with first differences (A078147): %e A376595 4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, 4, 4, 3, ... %e A376595 with first differences (A376593): %e A376595 -3, 2, 1, -2, 0, 2, -3, 1, -1, 3, 0, 0, 0, -3, 2, -2, 0, 1, 0, 0, 2, -1, -2, 3, ... %e A376595 with nonzeros (A376594) at: %e A376595 1, 2, 3, 4, 6, 7, 8, 9, 10, 14, 15, 16, 18, 21, 22, 23, 24, 26, 27, 28, 29, 30, ... %t A376595 Join@@Position[Sign[Differences[Select[Range[100],!SquareFreeQ[#]&],2]],1|-1] %Y A376595 The first differences were A078147. %Y A376595 These are the nonzeros of A376593. %Y A376595 The complement is A376594. %Y A376595 A000040 lists the prime numbers, differences A001223. %Y A376595 A005117 lists squarefree numbers, differences A076259. %Y A376595 A013929 lists nonsquarefree numbers, differences A078147. %Y A376595 A114374 counts integer partitions into nonsquarefree numbers. %Y A376595 For points of nonzero curvature: A333214 (prime), A376603 (composite), A376589 (non-perfect-power), A376592 (squarefree), A376598 (prime-power), A376601 (non-prime-power). %Y A376595 For nonsquarefree numbers: A078147 (first differences), A376593 (second differences), A376594 (inflections and undulations). %Y A376595 Cf. A007674, A036263, A053797, A053806, A061398, A120992, A373198, A375707, A376306, A376312, A376590. %K A376595 nonn %O A376595 1,2 %A A376595 _Gus Wiseman_, Oct 04 2024