cp's OEIS Frontend

A378373 Number of composite numbers (A002808) between consecutive nonsquarefree numbers (A013929), exclusive.

%I A378373 #6 Dec 02 2024 10:10:34
%S A378373 1,0,1,2,0,0,2,0,1,0,1,3,2,1,0,1,0,0,1,0,1,2,1,0,2,2,1,0,2,0,1,3,0,1,
%T A378373 3,0,0,0,1,2,2,2,0,2,0,2,0,0,0,2,2,0,1,3,2,0,0,0,0,2,2,1,0,2,0,1,0,1,
%U A378373 0,2,2,3,0,1,2,0,0,3,2,0,2,3,3,2,0,1,2
%N A378373 Number of composite numbers (A002808) between consecutive nonsquarefree numbers (A013929), exclusive.
%C A378373 All terms are 0, 1, 2, or 3 (cf. A078147).
%C A378373 The inclusive version is a(n) + 2.
%C A378373 The nonsquarefree numbers begin: 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, ...
%e A378373 The composite numbers counted by a(n) form the following set partition of A120944:
%e A378373 {6}, {}, {10}, {14,15}, {}, {}, {21,22}, {}, {26}, {}, {30}, {33,34,35}, {38,39}, ...
%t A378373 v=Select[Range[100],!SquareFreeQ[#]&];
%t A378373 Table[Length[Select[Range[v[[i]]+1,v[[i+1]]-1],CompositeQ]],{i,Length[v]-1}]
%Y A378373 For prime (instead of nonsquarefree) we have A046933.
%Y A378373 For squarefree (instead of nonsquarefree) we have A076259(n)-1.
%Y A378373 For prime power (instead of nonsquarefree) we have A093555.
%Y A378373 For prime instead of composite we have A236575.
%Y A378373 For nonprime prime power (instead of nonsquarefree) we have A378456.
%Y A378373 For perfect power (instead of nonsquarefree) we have A378614, primes A080769.
%Y A378373 A002808 lists the composite numbers.
%Y A378373 A005117 lists the squarefree numbers, differences A076259.
%Y A378373 A013929 lists the nonsquarefree numbers, differences A078147.
%Y A378373 A073247 lists squarefree numbers with nonsquarefree neighbors.
%Y A378373 A120944 lists squarefree composite numbers.
%Y A378373 A377432 counts perfect-powers between primes, zeros A377436.
%Y A378373 A378369 gives distance to the next nonsquarefree number (A120327).
%Y A378373 Cf. A065890, A067535, A067871, A080101, A081221, A151800, A243348, A366833, A377046, A378033, A378039, A378086.
%K A378373 nonn
%O A378373 1,4
%A A378373 _Gus Wiseman_, Dec 02 2024