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A378087 First-differences of A067535 (least positive integer >= n that is squarefree).

%I A378087 #8 Nov 22 2024 11:08:25
%S A378087 1,1,2,0,1,1,3,0,0,1,2,0,1,1,2,0,2,0,2,0,1,1,3,0,0,3,0,0,1,1,2,0,1,1,
%T A378087 2,0,1,1,2,0,1,1,3,0,0,1,4,0,0,0,2,0,2,0,2,0,1,1,2,0,1,3,0,0,1,1,2,0,
%U A378087 1,1,2,0,1,3,0,0,1,1,3,0,0,1,2,0,1,1,2
%N A378087 First-differences of A067535 (least positive integer >= n that is squarefree).
%C A378087 Does this contain all nonnegative integers? The positions of first appearances begin: 4, 1, 3, 7, 47, 241, 843, 22019, 217069, ...
%t A378087 Differences[Table[NestWhile[#+1&,n,#>1&&!SquareFreeQ[#]&],{n,100}]]
%Y A378087 Ones are A007674.
%Y A378087 Zeros are A013929, complement A005117.
%Y A378087 Positions of first appearances are A020754 (except first term) = A045882 - 1.
%Y A378087 First-differences of A067535.
%Y A378087 Twos are A280892.
%Y A378087 For prime-powers we have A377780, differences of A000015.
%Y A378087 The nonsquarefree opposite is A378036, differences of A378033.
%Y A378087 The restriction to primes + 1 is A378037 (opposite A378038), differences of A112926.
%Y A378087 For nonsquarefree numbers we have A378039, see A377783, A377784, A378040.
%Y A378087 The opposite is A378085, differences of A070321.
%Y A378087 A000040 lists the primes, differences A001223, seconds A036263.
%Y A378087 A005117 lists the squarefree numbers.
%Y A378087 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A378087 A061398 counts squarefree numbers between primes, zeros A068360.
%Y A378087 A061399 counts nonsquarefree numbers between primes, zeros A068361.
%Y A378087 Cf. A005117, A007675, A068781, A073247, A073248, A378084.
%Y A378087 Cf. A013928, A053797, A053806, A072284, A120327, A224363.
%K A378087 nonn
%O A378087 1,3
%A A378087 _Gus Wiseman_, Nov 20 2024