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%I #24 Sep 10 2020 09:28:45
%S 1,2,20,90,272,650,1332,4160,6642,10100,14762,20880,28730,38612,50850,
%T 65792,83810,130682,160400,194922,234740,280370,332352,391250,457652,
%U 532170,615440,708122,810900,924482,1187010,1337492,1501850,1680912,1875530,2314962,2561600
%N Numbers k such that core(k) = ceiling(sqrt(k)) where core(k) is the squarefree part of k (the smallest integer such that k*core(k) is a square).
%C Conjecture: sequence is A071253 minus those entries of A071253 that have their index in A049532, i.e., a(n) is of form n^2*(n^2+1) for all n not in A049532. - _Ralf Stephan_, Aug 18 2004
%H Amiram Eldar, <a href="/A069187/b069187.txt">Table of n, a(n) for n = 1..300</a>
%t core[n_] := Times @@ Apply[ Power, {#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[n], {1}]; Select[Range[500000], core[#] == Ceiling[Sqrt[#]]&] (* _Jean-François Alcover_, Jul 26 2011 *)
%Y Cf. A007913, A049532, A071253.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Apr 14 2002
%E More terms from _Amiram Eldar_, Sep 10 2020
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