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

1,2

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

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 *)

Prog

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

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.

Sequence in context: A182996 A325378 A164596 * A381736 A131647 A301900

Adjacent sequences: A295099 A295100 A295101 * A295103 A295104 A295105

Keyword

nonn

Author

Max Alekseyev, Nov 14 2017

Status

approved