cp's OEIS Frontend

A053806 Numbers where a gap begins in the sequence of squarefree numbers (A005117).

%I A053806 #24 Nov 10 2023 09:09:37
%S A053806 4,8,12,16,18,20,24,27,32,36,40,44,48,52,54,56,60,63,68,72,75,80,84,
%T A053806 88,90,92,96,98,104,108,112,116,120,124,128,132,135,140,144,147,150,
%U A053806 152,156,160,162,164,168,171,175,180,184,188,192,196,198,200,204,207,212
%N A053806 Numbers where a gap begins in the sequence of squarefree numbers (A005117).
%H A053806 Charles R Greathouse IV, <a href="/A053806/b053806.txt">Table of n, a(n) for n = 1..10000</a>
%H A053806 M. Filaseta and O. Trifonov, <a href="http://dx.doi.org/10.1007/978-1-4612-3464-7_15">On Gaps between Squarefree Numbers</a>. In Analytic Number Theory, Vol 85, 1990, Birkhäuser, Basel, pp. 235-253.
%H A053806 E. Fogels, <a href="http://dx.doi.org/10.1017/S0305004100017990">On the average values of arithmetic functions</a>, Proc. Cambridge Philos. Soc. 1941, 37: 358-372.
%H A053806 L. Marmet, <a href="http://www.marmet.org/louis/sqfgap/">First occurrences of squarefree gaps...</a>
%H A053806 L. Marmet, <a href="http://arxiv.org/abs/1210.3829">First occurrences of square-free gaps and an algorithm for their computation</a>, arXiv preprint arXiv:1210.3829 [math.NT], 2012.
%H A053806 K. F. Roth, <a href="http://jlms.oxfordjournals.org/content/s1-26/4/263.extract">On the gaps between squarefree numbers</a>, J. London Math. Soc. 1951 (2) 26:263-268.
%e A053806 The first gap is at 4 and has length 1; the next starts at 8 and has length 2 (since neither 8 nor 9 are squarefree).
%o A053806 (PARI) is(n)=!issquarefree(n) && issquarefree(n-1) \\ _Charles R Greathouse IV_, Nov 05 2017
%o A053806 (PARI) list(lim)=my(v=List(),t); forfactored(n=4,lim\1, if(vecmax(n[2][,2])>1, if(!t, listput(v,n[1])); t=1, t=0)); Vec(v) \\ _Charles R Greathouse IV_, Nov 05 2017
%Y A053806 Cf. A005117, A053797, A045882, A051681, A013929.
%K A053806 nonn,easy
%O A053806 1,1
%A A053806 _N. J. A. Sloane_, Apr 07 2000