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%I #10 Jul 04 2022 04:38:40
%S 8,24,48,49,63,80,120,125,168,175,195,224,242,288,324,350,351,360,363,
%T 374,384,399,440,441,455,475,494,512,528,539,560,575,594,624,675,714,
%U 728,735,759,832,840,874,896,935,960,968,1000,1014,1023,1044,1053,1088,1104
%N Numbers k such that k is sqrt(k)-smooth and k+1 is sqrt(k+1)-smooth.
%C Numbers k such that k and k+1 are both in A048098.
%C This sequence is infinite: if p is an odd prime then p^2-1 is a term.
%H Amiram Eldar, <a href="/A355433/b355433.txt">Table of n, a(n) for n = 1..10000</a>
%e 8 is a term since 8 is sqrt(8)-smooth (2^2 <= 8) and 9 is sqrt(9)-smooth (3^2 <= 9).
%t smQ[n_] := FactorInteger[n][[-1, 1]]^2 <= n; Select[Range[1000], smQ[#] && smQ[# + 1] &]
%Y Cf. A048098, A355434.
%Y Subsequences: A084920 \ {3}, A060355, A348119.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jul 02 2022
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