A071311 Squarefree numbers k with largest prime factor = floor(sqrt(k)).

30, 182, 195, 399, 870, 1023, 1406, 1443, 1722, 2915, 3782, 4623, 5402, 7055, 8099, 10302, 10815, 11990, 12099, 12882, 12995, 16383, 17423, 18906, 19599, 24806, 24963, 26895, 30102, 32942, 33123, 37442, 37635, 39999, 44943, 52670, 52899, 54755, 63503, 66306, 66563

Offset

1,1

Comments

If k = p(1)*p(2)*...p(r) is in the sequence, where p(r) is the largest prime factor, then p(1)*p(2)*...*p(r-1) - p(r) = 1 or 2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1023 = 3*11*31 and sqrt(1023) = 31.98437... hence 1023 is in the sequence.

Mathematica

Select[Range[2, 50000], SquareFreeQ[#] && FactorInteger[#][[-1, 1]] == Floor[Sqrt[#]] &] (* Amiram Eldar, Apr 23 2022 *)

Prog

(PARI) for(n=2, 100000, if(issquarefree(n)*component(component(factor(n), 1), omega(n))==floor(sqrt(n)), print1(n, ", ")))

Crossrefs

Intersection of A005117 and A071835.

Sequence in context: A281999 A156318 A042758 * A337494 A265037 A249001

Adjacent sequences: A071308 A071309 A071310 * A071312 A071313 A071314

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 11 2002

Status

approved