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A378084 Nonsquarefree numbers not appearing in A377783 (least nonsquarefree number > prime(n)).

%I A378084 #5 Nov 24 2024 22:49:04
%S A378084 9,25,27,28,36,45,49,50,52,56,64,76,81,88,92,96,99,100,117,120,121,
%T A378084 124,125,126,135,136,144,147,148,153,156,162,169,171,172,176,188,189,
%U A378084 204,207,208,216,220,225,236,243,244,245,248,250,256,261,268,275,276,280
%N A378084 Nonsquarefree numbers not appearing in A377783 (least nonsquarefree number > prime(n)).
%C A378084 Warning: do not confuse with A377784.
%F A378084 Complement of A378040 in A013929.
%e A378084 The terms together with their prime indices begin:
%e A378084     9: {2,2}
%e A378084    25: {3,3}
%e A378084    27: {2,2,2}
%e A378084    28: {1,1,4}
%e A378084    36: {1,1,2,2}
%e A378084    45: {2,2,3}
%e A378084    49: {4,4}
%e A378084    50: {1,3,3}
%e A378084    52: {1,1,6}
%e A378084    56: {1,1,1,4}
%e A378084    64: {1,1,1,1,1,1}
%e A378084    76: {1,1,8}
%e A378084    81: {2,2,2,2}
%e A378084    88: {1,1,1,5}
%e A378084    92: {1,1,9}
%e A378084    96: {1,1,1,1,1,2}
%t A378084 nn=100;
%t A378084 y=Table[NestWhile[#+1&,Prime[n],SquareFreeQ[#]&],{n,nn}];
%t A378084 Complement[Select[Range[Prime[nn]],!SquareFreeQ[#]&],y]
%Y A378084 Disjoint from A377783 (union A378040), first-differences A377784.
%Y A378084 Appearing once: A378082.
%Y A378084 Appearing twice: A378083.
%Y A378084 A000040 lists the primes, differences A001223, seconds A036263.
%Y A378084 A005117 lists the squarefree numbers.
%Y A378084 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A378084 A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.
%Y A378084 A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.
%Y A378084 A070321 gives the greatest squarefree number up to n.
%Y A378084 A112925 gives least squarefree number > prime(n), differences A378038.
%Y A378084 A112926 gives greatest squarefree number < prime(n), differences A378037.
%Y A378084 A120327 (union A162966) gives least nonsquarefree number >= n, differences A378039.
%Y A378084 A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.
%Y A378084 Cf. A053797, A053806, A072284, A224363, A377430, A377431, A378032, A378033.
%K A378084 nonn
%O A378084 1,1
%A A378084 _Gus Wiseman_, Nov 23 2024