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A053806
Numbers where a gap begins in the sequence of squarefree numbers (A005117).
48
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
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, Birkhäuser, 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 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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 07 2000
STATUS
approved