cp's OEIS Frontend

A376264 Run-sums of first differences (A078147) of nonsquarefree numbers (A013929).

%I A376264 #10 Sep 27 2024 12:00:13
%S A376264 4,1,3,4,4,4,1,2,1,16,1,3,2,6,4,3,1,8,3,1,4,1,3,4,4,4,2,2,16,1,3,1,3,
%T A376264 2,2,4,3,1,8,3,1,4,1,3,4,4,4,1,2,1,3,1,12,1,3,4,4,4,3,1,16,1,3,4,4,4,
%U A376264 2,3,3,4,8,1,3,4,4,3,1,3,1,8,1,3,4,1,3,4
%N A376264 Run-sums of first differences (A078147) of nonsquarefree numbers (A013929).
%C A376264 Does the image include all positive integers? I have only verified this up to 8.
%e A376264 The sequence of nonsquarefree numbers (A013929) is:
%e A376264   4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ...
%e A376264 with first differences (A078147):
%e A376264   4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ...
%e A376264 with runs:
%e A376264   (4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ...
%e A376264 with sums (A376264):
%e A376264   4, 1, 3, 4, 4, 4, 1, 2, 1, 16, 1, 3, 2, 6, 4, 3, 1, 8, 3, 1, 4, 1, 3, 4, ...
%t A376264 Total/@Split[Differences[Select[Range[1000],!SquareFreeQ[#]&]]]//Most
%Y A376264 Before taking run-sums we had A078147.
%Y A376264 For nonprime instead of nonsquarefree numbers we have A373822.
%Y A376264 Positions of first appearances are A376265, sorted A376266.
%Y A376264 For run-lengths instead of run-sums we have A376267.
%Y A376264 For squarefree instead of nonsquarefree we have A376307.
%Y A376264 For prime-powers instead of nonsquarefree numbers we have A376310.
%Y A376264 For compression instead of run-sums we have A376312.
%Y A376264 A000040 lists the prime numbers, differences A001223.
%Y A376264 A000961 and A246655 list prime-powers, differences A057820.
%Y A376264 A003242 counts compressed compositions, ranks A333489.
%Y A376264 A005117 lists squarefree numbers, differences A076259 (ones A375927).
%Y A376264 A013929 lists nonsquarefree numbers, differences A078147.
%Y A376264 Cf. A053797, A053806, A061398, A072284, A120992, A373197, A373413, A375707, A376305, A376306, A376311.
%K A376264 nonn
%O A376264 1,1
%A A376264 _Gus Wiseman_, Sep 26 2024