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Maximum of the n-th maximal run of nonsquarefree numbers (increasing by 1 at a time).
2

%I #6 Sep 16 2024 22:04:04

%S 4,9,12,16,18,20,25,28,32,36,40,45,50,52,54,56,60,64,68,72,76,81,84,

%T 88,90,92,96,100,104,108,112,117,121,126,128,132,136,140,144,148,150,

%U 153,156,160,162,164,169,172,176,180,184,189,192,196,198,200,204,208

%N Maximum of the n-th maximal run of nonsquarefree numbers (increasing by 1 at a time).

%e The maximal runs of nonsquarefree numbers begin:

%e 4

%e 8 9

%e 12

%e 16

%e 18

%e 20

%e 24 25

%e 27 28

%e 32

%e 36

%e 40

%e 44 45

%e 48 49 50

%t Max/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1==#2&]//Most

%Y For length instead of maximum we have A053797 (firsts A373199).

%Y For lengths of anti-runs we have A373409 (firsts A373573).

%Y For sum instead of maximum we have A373414, anti A373412.

%Y For minimum instead of maximum we have A053806, anti A373410.

%Y For anti-runs instead of runs we have A068781.

%Y For squarefree instead of nonsquarefree we have A373415, anti A007674.

%Y For nonprime instead of nonsquarefree we have A006093 with 2 removed.

%Y A005117 lists the squarefree numbers, first differences A076259.

%Y A013929 lists the nonsquarefree numbers, differences A078147, sums A329472.

%Y A061398 counts squarefree numbers between primes, nonsquarefree A061399.

%Y A120992 gives squarefree run-lengths, anti A373127 (firsts A373128).

%Y A373413 adds up each maximal run of squarefree numbers, min A072284.

%Y A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

%Y Cf. A000040, A020754, A045882, A049094, A054265, A077641, A101836, A143658, A294242, A375709.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 15 2024