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A376164 Maximum of the n-th maximal run of nonsquarefree numbers (increasing by 1 at a time).

%I A376164 #6 Sep 16 2024 22:04:04
%S A376164 4,9,12,16,18,20,25,28,32,36,40,45,50,52,54,56,60,64,68,72,76,81,84,
%T A376164 88,90,92,96,100,104,108,112,117,121,126,128,132,136,140,144,148,150,
%U A376164 153,156,160,162,164,169,172,176,180,184,189,192,196,198,200,204,208
%N A376164 Maximum of the n-th maximal run of nonsquarefree numbers (increasing by 1 at a time).
%e A376164 The maximal runs of nonsquarefree numbers begin:
%e A376164        4
%e A376164      8   9
%e A376164       12
%e A376164       16
%e A376164       18
%e A376164       20
%e A376164     24  25
%e A376164     27  28
%e A376164       32
%e A376164       36
%e A376164       40
%e A376164     44  45
%e A376164   48  49  50
%t A376164 Max/@Split[Select[Range[100],!SquareFreeQ[#]&],#1+1==#2&]//Most
%Y A376164 For length instead of maximum we have A053797 (firsts A373199).
%Y A376164 For lengths of anti-runs we have A373409 (firsts A373573).
%Y A376164 For sum instead of maximum we have A373414, anti A373412.
%Y A376164 For minimum instead of maximum we have A053806, anti A373410.
%Y A376164 For anti-runs instead of runs we have A068781.
%Y A376164 For squarefree instead of nonsquarefree we have A373415, anti A007674.
%Y A376164 For nonprime instead of nonsquarefree we have A006093 with 2 removed.
%Y A376164 A005117 lists the squarefree numbers, first differences A076259.
%Y A376164 A013929 lists the nonsquarefree numbers, differences A078147, sums A329472.
%Y A376164 A061398 counts squarefree numbers between primes, nonsquarefree A061399.
%Y A376164 A120992 gives squarefree run-lengths, anti A373127 (firsts A373128).
%Y A376164 A373413 adds up each maximal run of squarefree numbers, min A072284.
%Y A376164 A375707 counts squarefree numbers between consecutive nonsquarefree numbers.
%Y A376164 Cf. A000040, A020754, A045882, A049094, A054265, A077641, A101836, A143658, A294242, A375709.
%K A376164 nonn
%O A376164 1,1
%A A376164 _Gus Wiseman_, Sep 15 2024