A295102 Squarefree numbers n that are sqrt(n)-smooth: if prime p|n then p^2 <= n.

1, 30, 70, 105, 154, 165, 182, 195, 210, 231, 273, 286, 330, 357, 374, 385, 390, 399, 418, 429, 442, 455, 462, 494, 510, 546, 561, 570, 595, 598, 627, 646, 663, 665, 690, 714, 715, 741, 759, 770, 782, 798, 805, 858, 870, 874, 897, 910, 935, 957, 966, 969

Offset: 1

Author

Max Alekseyev, Nov 14 2017

Keywords

• nonn

Comments

If n is in the sequence and m < n is squarefree and coprime to n, then m*n is in the sequence. - Robert Israel, Aug 12 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Squarefree terms of A048098, and also of A063539.

Besides initial 1, subsequence of A164596.

Together with A001248, forms indices of records in A295101.

Cf. A005117.

Programs

Maple

filter:= proc(n) local t;
  andmap(t -> t[2]=1 and t[1]^2<=n, ifactors(n)[2])
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 12 2019

Mathematica

selQ[n_] := SquareFreeQ[n] && AllTrue[FactorInteger[n][[All, 1]], #^2<=n&];
Select[Range[1000], selQ] (* Jean-François Alcover, Jul 30 2020 *)

PARI

isok(n) = (n==1) || (issquarefree(n) && (vecmax(factor(n)[,1])^2 < n)); \\ Michel Marcus, Aug 12 2019