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

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 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: A355740 A371089 A370348 * A068306 A311118 A348705

Adjacent sequences: A053803 A053804 A053805 * A053807 A053808 A053809

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 07 2000

Status

approved