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 A376600 #6 Oct 05 2024 14:00:18 %S A376600 2,7,9,10,11,14,15,18,20,22,24,26,29,30,31,33,39,41,43,44,45,47,48,50, %T A376600 51,52,55,56,57,58,59,62,64,66,68,70,73,74,75,76,77,80,86,87,88,90,92, %U A376600 93,94,95,96,97,98,100,102,103,104,107,108,109,112,114,116 %N A376600 Inflection or undulation points in the sequence of non-prime-powers inclusive (A024619). %C A376600 These are points at which the second differences (A376599) are zero. %C A376600 Inclusive means 1 is a prime-power but not a non-prime-power. For the exclusive version, add 1 to all terms. %H A376600 Gus Wiseman, <a href="/A376600/a376600.png">Inflection and undulation points in the non-prime-powers inclusive</a>. %e A376600 The non-prime-powers inclusive are (A024619): %e A376600 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, ... %e A376600 with first differences (A375735): %e A376600 4, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, ... %e A376600 with first differences (A376599): %e A376600 -2, 0, -1, 2, -1, -1, 0, 1, 0, 0, 0, 1, -2, 0, 0, 1, -1, 0, 1, 0, -1, 0, 1, 0, ... %e A376600 with zeros at (A376600): %e A376600 2, 7, 9, 10, 11, 14, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 39, 41, 43, 44, ... %t A376600 Join@@Position[Differences[Select[Range[100], !(#==1||PrimePowerQ[#])&],2],0] %Y A376600 For first differences we had A375735, ones A375713(n)-1. %Y A376600 These are the zeros of A376599. %Y A376600 The complement is A376601. %Y A376600 A000961 lists prime-powers inclusive, exclusive A246655. %Y A376600 A001597 lists perfect-powers, complement A007916. %Y A376600 A024619/A361102 list non-prime-powers inclusive. %Y A376600 A321346/A321378 count integer partitions into non-prime-powers, factorizations A322452. %Y A376600 For non-prime-powers: A375735/A375708 (first differences), A376599 (second differences), A376601 (nonzero curvature). %Y A376600 For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376596 (prime-power). %Y A376600 Cf. A025475, A053707, A057820, A064113, A093555, A174965, A251092, A333254, A376653, A376654. %K A376600 nonn %O A376600 1,1 %A A376600 _Gus Wiseman_, Oct 05 2024