A140715 Consider all the integers k where the n-th prime <= k <= the (n+1)th prime. a(n) is the largest integer that divides at least two of the integers k.

1, 1, 1, 2, 1, 2, 1, 2, 4, 1, 4, 2, 1, 2, 4, 3, 1, 3, 2, 1, 3, 2, 4, 6, 2, 1, 2, 1, 2, 9, 2, 4, 1, 7, 1, 4, 3, 2, 4, 3, 1, 7, 1, 2, 1, 10, 6, 2, 1, 2, 3, 1, 5, 4, 3, 4, 1, 4, 2, 1, 5, 9, 2, 1, 2, 11, 4, 5, 1, 2, 3, 6, 4, 3, 2, 4, 6, 2, 6, 5, 1, 5, 1, 3, 2, 4, 6, 2, 1, 2, 9, 6, 2, 6, 2, 4, 10, 1, 15, 3, 5, 3, 4

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The 18th prime is 61 and the 19th prime is 67. So we will consider the integers 61, 62, 63, 64, 65, 66, 67. No integer >= 7 divides more than one integer in this range, because the range consists only of 7 terms, the two on the end being prime. Checking: 6 divides 66, but does not divide any other integer in this range. 5 divides 65, but does not divide any other integer in this range. 4 divides 64, but nothing else. 3, on the other hand, divides both 63 and 66. So a(18) = 3.

Maple

nodvs := proc(n, L) local a, l ; a := 0 ; for l in L do if l mod n = 0 then a := a+1 ; fi: od: RETURN(a) ; end: A140715 := proc(n) local k, a ; k := [seq(i, i=ithprime(n)..ithprime(n+1))] ; for a from op(-1, k) by -1 do if nodvs(a, k) >= 2 then RETURN(a) ; fi; od: end: for n from 1 to 160 do printf("%d, ", A140715(n)) ; od: # R. J. Mathar, Aug 08 2008

Mathematica

lid2[{a_, b_}]:=Module[{r=Range[a, b]}, Select[Table[{n, Count[r/n, _?IntegerQ]}, {n, Length[r], 1, -1}], #[[2]]>1&, 1][[1, 1]]]; lid2/@Partition[Prime[ Range[ 110]], 2, 1] (* Harvey P. Dale, Jun 07 2013 *)

Crossrefs

Sequence in context: A347224 A339270 A345226 * A330690 A263143 A197945

Adjacent sequences: A140712 A140713 A140714 * A140716 A140717 A140718

Keyword

nonn

Author

Leroy Quet, Jul 11 2008

Extensions

Extended beyond a(18) by R. J. Mathar, Aug 08 2008

Status

approved