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 A376601 #6 Oct 05 2024 14:00:14 %S A376601 1,3,4,5,6,8,12,13,16,17,19,21,23,25,27,28,32,34,35,36,37,38,40,42,46, %T A376601 49,53,54,60,61,63,65,67,69,71,72,78,79,81,82,83,84,85,89,91,99,101, %U A376601 105,106,110,111,113,115,117,118,122,124,132,134,136,138,148 %N A376601 Points of nonzero curvature in the sequence of non-prime-powers inclusive (A024619). %C A376601 These are points at which the second differences (A376599) are nonzero. %C A376601 Inclusive means 1 is a prime-power but not a non-prime-power. For the exclusive version, subtract 1 and shift left. %H A376601 Gus Wiseman, <a href="/A376601/a376601.png">Points of nonzero curvature in the non-prime-powers inclusive</a>. %e A376601 The non-prime-powers inclusive (A024619) are: %e A376601 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, ... %e A376601 with first differences (A375735): %e A376601 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 A376601 with first differences (A376599): %e A376601 -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 A376601 with nonzero terms (A376601) at: %e A376601 1, 3, 4, 5, 6, 8, 12, 13, 16, 17, 19, 21, 23, 25, 27, 28, 32, 34, 35, 36, 37, ... %t A376601 Join@@Position[Sign[Differences[Select[Range[100], !(#==1||PrimePowerQ[#])&],2]],1|-1] %Y A376601 For first differences we had A375735, ones A375713(n) - 1. %Y A376601 These are the nonzeros of A376599. %Y A376601 The complement is A376600. %Y A376601 A000961 lists prime-powers inclusive, exclusive A246655. %Y A376601 A007916 lists non-perfect-powers. %Y A376601 A024619/A361102 list non-prime-powers inclusive. %Y A376601 A057820 gives first differences of prime-powers inclusive. %Y A376601 A321346/A321378 count integer partitions into non-prime-powers, factorizations A322452. %Y A376601 For non-prime-powers: A375735/A375708 (first differences), A376599 (second differences), A376600 (inflections and undulations). %Y A376601 For nonzero curvature: A333214 (prime), A376603 (composite), A376588 (non-perfect-power), A376592 (squarefree), A376595 (nonsquarefree), A376598 (prime-power). %Y A376601 Cf. A025475, A053707, A064113, A093555, A174965, A251092, A333254, A376653, A376654. %K A376601 nonn %O A376601 1,2 %A A376601 _Gus Wiseman_, Oct 05 2024