%I #18 Nov 17 2018 21:02:50
%S 3,5,6,10,13,14,19,21,26,30,33,38,42,46,51,55,61,62,69,73,74,82,85,91,
%T 101,102,105,109,110,114,129,133,138,141,151,154,158,165,170,174,181,
%U 182,193,194,199,201,213,226,229,230,235,241,246,253,258,265,271,273
%N Smallest squarefree integer > the n-th prime.
%H Michael De Vlieger, <a href="/A112926/b112926.txt">Table of n, a(n) for n = 1..10000</a>
%e 10 is the smallest squarefree number greater than the 4th prime, 7. So a(4) = 10.
%p with(numtheory): a:=proc(n) local p,B,j: p:=ithprime(n): B:={}: for j from p+1 to p+20 do if abs(mobius(j))>0 then B:=B union {j} else B:=B fi od: B[1] end: seq(a(m),m=1..75); # _Emeric Deutsch_, Oct 10 2005
%t Do[k = Prime[n] + 1; While[ !SquareFreeQ[k], k++ ]; Print[k], {n, 1, 100}] (* _Ryan Propper_, Oct 10 2005 *)
%t With[{k = 120}, Table[SelectFirst[Range[Prime@ n + 1, Prime@ n + k], SquareFreeQ], {n, 58}]] (* _Michael De Vlieger_, Aug 16 2017 *)
%o (PARI) a(n,p=prime(n))=while(!issquarefree(p++),); p \\ _Charles R Greathouse IV_, Aug 16 2017
%Y Cf. A061400, A112925, A112928, A112929, A112930.
%K nonn
%O 1,1
%A _Leroy Quet_, Oct 06 2005
%E More terms from _Ryan Propper_ and _Emeric Deutsch_, Oct 10 2005