cp's OEIS Frontend

A376307 Run-sums of the sequence of first differences of squarefree numbers.

%I A376307 #10 Sep 21 2024 19:19:09
%S A376307 2,2,2,3,1,2,2,6,2,6,2,2,2,2,2,2,2,3,1,4,6,2,2,1,3,2,2,2,2,1,3,2,3,1,
%T A376307 2,2,6,2,2,4,2,2,2,2,2,2,2,3,1,3,1,4,2,2,2,1,3,2,2,2,2,1,3,2,3,1,2,2,
%U A376307 6,2,6,1,3,2,2,2,2,2,3,1,2,2,6,2,2,1,3
%N A376307 Run-sums of the sequence of first differences of squarefree numbers.
%e A376307 The sequence of squarefree numbers (A005117) is:
%e A376307   1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...
%e A376307 The sequence of first differences (A076259) of squarefree numbers is:
%e A376307   1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...
%e A376307 with runs:
%e A376307   (1,1),(2),(1,1),(3),(1),(2),(1,1),(2,2,2),(1,1),(3,3),(1,1),(2),(1,1), ...
%e A376307 with sums A376307 (this sequence).
%t A376307 Total/@Split[Differences[Select[Range[100],SquareFreeQ]]]
%Y A376307 Run-sums of first differences of A005117.
%Y A376307 Before taking run-sums we had A076259, ones A375927.
%Y A376307 For the squarefree numbers themselves we have A373413.
%Y A376307 For prime instead of squarefree numbers we have A373822, halved A373823.
%Y A376307 For compression instead of run-sums we have A376305, ones A376342.
%Y A376307 For run-lengths instead of run-sums we have A376306.
%Y A376307 For prime-powers instead of squarefree numbers we have A376310.
%Y A376307 For positions of first appearances instead of run-sums we have A376311.
%Y A376307 A000040 lists the prime numbers, differences A001223.
%Y A376307 A000961 and A246655 list prime-powers, first differences A057820.
%Y A376307 A003242 counts compressed or anti-run compositions, ranks A333489.
%Y A376307 A005117 lists squarefree numbers, differences A076259.
%Y A376307 A013929 lists nonsquarefree numbers, differences A078147.
%Y A376307 A116861 counts partitions by compressed sum, by compressed length A116608.
%Y A376307 A274174 counts contiguous compositions, ranks A374249.
%Y A376307 Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A373197, A373198, A375707.
%K A376307 nonn
%O A376307 1,1
%A A376307 _Gus Wiseman_, Sep 21 2024