OFFSET
1,1
COMMENTS
Does the image include all positive integers? I have only verified this up to 8.
EXAMPLE
The sequence of nonsquarefree numbers (A013929) is:
4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ...
with first differences (A078147):
4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ...
with runs:
(4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ...
with sums (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, ...
MATHEMATICA
Total/@Split[Differences[Select[Range[1000], !SquareFreeQ[#]&]]]//Most
CROSSREFS
Before taking run-sums we had A078147.
For nonprime instead of nonsquarefree numbers we have A373822.
For run-lengths instead of run-sums we have A376267.
For squarefree instead of nonsquarefree we have A376307.
For prime-powers instead of nonsquarefree numbers we have A376310.
For compression instead of run-sums we have A376312.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 26 2024
STATUS
approved