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

%I A295102 #17 Jul 30 2020 07:17:53
%S A295102 1,30,70,105,154,165,182,195,210,231,273,286,330,357,374,385,390,399,
%T A295102 418,429,442,455,462,494,510,546,561,570,595,598,627,646,663,665,690,
%U A295102 714,715,741,759,770,782,798,805,858,870,874,897,910,935,957,966,969
%N A295102 Squarefree numbers n that are sqrt(n)-smooth: if prime p|n then p^2 <= n.
%C A295102 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
%H A295102 Robert Israel, <a href="/A295102/b295102.txt">Table of n, a(n) for n = 1..10000</a>
%p A295102 filter:= proc(n) local t;
%p A295102   andmap(t -> t[2]=1 and t[1]^2<=n, ifactors(n)[2])
%p A295102 end proc:
%p A295102 select(filter, [$1..1000]); # _Robert Israel_, Aug 12 2019
%t A295102 selQ[n_] := SquareFreeQ[n] && AllTrue[FactorInteger[n][[All, 1]], #^2<=n&];
%t A295102 Select[Range[1000], selQ] (* _Jean-François Alcover_, Jul 30 2020 *)
%o A295102 (PARI) isok(n) = (n==1) || (issquarefree(n) && (vecmax(factor(n)[,1])^2 < n)); \\ _Michel Marcus_, Aug 12 2019
%Y A295102 Squarefree terms of A048098, and also of A063539.
%Y A295102 Besides initial 1, subsequence of A164596.
%Y A295102 Together with A001248, forms indices of records in A295101.
%Y A295102 Cf. A005117.
%K A295102 nonn
%O A295102 1,2
%A A295102 _Max Alekseyev_, Nov 14 2017