A376164 - OEIS

A376164

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

4, 9, 12, 16, 18, 20, 25, 28, 32, 36, 40, 45, 50, 52, 54, 56, 60, 64, 68, 72, 76, 81, 84, 88, 90, 92, 96, 100, 104, 108, 112, 117, 121, 126, 128, 132, 136, 140, 144, 148, 150, 153, 156, 160, 162, 164, 169, 172, 176, 180, 184, 189, 192, 196, 198, 200, 204, 208

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The maximal runs of nonsquarefree numbers begin:

8 9

24 25

27 28

44 45

48 49 50

MAPLE

state:= 0:

R:= NULL: count:= 0:

for i from 4 while count < 100 do

if not numtheory:-issqrfree(i) then state:= 1

elif state = 1 then R:= R, i-1; count:= count+1; state:= 0

od:

R; # Robert Israel, Sep 15 2025

MATHEMATICA

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

CROSSREFS

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

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

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

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

For anti-runs instead of runs we have A068781.

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

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

A005117 lists the squarefree numbers, first differences A076259.

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

A061398 counts squarefree numbers between primes, nonsquarefree A061399.

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

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

A375707 counts squarefree numbers between consecutive nonsquarefree numbers.

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

Sequence in context: A094120 A066423 A355571 * A072498 A162643 A072587

Adjacent sequences: A376161 A376162 A376163 * A376165 A376166 A376167

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 15 2024

STATUS

approved