A112925 Largest squarefree integer < the n-th prime.

1, 2, 3, 6, 10, 11, 15, 17, 22, 26, 30, 35, 39, 42, 46, 51, 58, 59, 66, 70, 71, 78, 82, 87, 95, 97, 102, 106, 107, 111, 123, 130, 134, 138, 146, 149, 155, 161, 166, 170, 178, 179, 190, 191, 195, 197, 210, 222, 226, 227, 231, 238, 239, 249, 255, 262, 267, 269, 274, 278

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

6 is the largest squarefree less than the 4th prime, 7. So a(4) = 6.

Maple

with(numtheory): a:=proc(n) local p, B, j: p:=ithprime(n): B:={}: for j from 1 to p-1 do if abs(mobius(j))>0 then B:=B union {j} else B:=B fi od: B[nops(B)] end: seq(a(m), m=1..75); # Emeric Deutsch, Oct 14 2005

Mathematica

With[{k = 120}, Table[SelectFirst[Range[Prime@ n - 1, Prime@ n - Min[Prime@ n - 1, k], -1], SquareFreeQ], {n, 60}]] (* Michael De Vlieger, Aug 16 2017 *)

Prog

(PARI) a(n, p=prime(n))=while(!issquarefree(p--), ); p \\ Charles R Greathouse IV, Aug 16 2017

Crossrefs

Cf. A061400, A112926, A112928, A112929, A112930.

Sequence in context: A286954 A047402 A088196 * A193246 A239012 A001635

Adjacent sequences: A112922 A112923 A112924 * A112926 A112927 A112928

Keyword

nonn

Author

Leroy Quet, Oct 06 2005

Extensions

More terms from Emeric Deutsch, Oct 14 2005

Status

approved