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 A053806 Numbers where a gap begins in the sequence of squarefree numbers (A005117). 8
 4, 8, 12, 16, 18, 20, 24, 27, 32, 36, 40, 44, 48, 52, 54, 56, 60, 63, 68, 72, 75, 80, 84, 88, 90, 92, 96, 98, 104, 108, 112, 116, 120, 124, 128, 132, 135, 140, 144, 147, 150, 152, 156, 160, 162, 164, 168, 171, 175, 180, 184, 188, 192, 196, 198, 200, 204, 207, 212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 M. Filaseta and O. Trifonov, On Gaps between Squarefree Numbers. In Analytic Number Theory, Vol 85, 1990, Birkhauser, Basel, pp. 235-253. E. Fogels, On the average values of arithmetic functions, Proc. Cambridge Philos. Soc. 1941, 37: 358-372. L. Marmet, First occurrences of squarefree gaps... L. Marmet, First occurrences of square-free gaps and an algorithm for their computation, arXiv preprint arXiv:1210.3829 [math.NT], 2012. K. F. Roth, On the gaps between squarefree numbers, J. London Math. Soc. 1951 (2) 26:263-268. EXAMPLE 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). PROG (PARI) is(n)=!issquarefree(n) && issquarefree(n-1) \\ Charles R Greathouse IV, Nov 05 2017 (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 CROSSREFS Cf. A005117, A053797, A045882, A051681, A013929. Sequence in context: A274919 A196032 A130702 * A068306 A311118 A272405 Adjacent sequences:  A053803 A053804 A053805 * A053807 A053808 A053809 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 07 2000 STATUS approved

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Last modified October 18 18:58 EDT 2018. Contains 316323 sequences. (Running on oeis4.)