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A364029 Odd squarefree semiprimes s = p*q such that (p + q)/2 and (p - q)/2 are squarefree.

%I A364029 #14 Jun 04 2024 07:39:48
%S A364029 21,35,51,69,85,91,93,123,133,187,213,219,221,235,237,253,259,267,339,
%T A364029 341,355,365,371,381,395,411,413,437,445,451,453,469,485,493,501,573,
%U A364029 611,635,667,669,685,699,723,731,755,763,771,779,781,789,803,813,843,851,893,899
%N A364029 Odd squarefree semiprimes s = p*q such that (p + q)/2 and (p - q)/2 are squarefree.
%H A364029 Robert Israel, <a href="/A364029/b364029.txt">Table of n, a(n) for n = 1..10000</a>
%p A364029 filter:= proc(n) local F,p,q;
%p A364029   F:= ifactors(n)[2];
%p A364029   if nops(F) <> 2 or F[1,2] <> 1 or F[2,2] <> 1 then return false fi;
%p A364029   p:= F[1,1]; q:= F[2,1];
%p A364029   numtheory:-issqrfree((p+q)/2) and numtheory:-issqrfree(abs(p-q)/2)
%p A364029 end proc:
%p A364029 select(filter, [seq(i,i=1..1000,2)]); # _Robert Israel_, Dec 12 2023
%t A364029 okQ[n_] := MatchQ[FactorInteger[n], {{p_, 1}, {q_, 1}} /; SquareFreeQ[(p + q)/2] && SquareFreeQ[(q - p)/2]];
%t A364029 Select[Range[1, 1000, 2], okQ] (* _Jean-François Alcover_, Jun 04 2024 *)
%o A364029 (PARI) forstep (k = 15, 900, 2, if (omega(k)==2 && bigomega(k)==2, my (F=factorint(k)); if ( issquarefree((F[2, 1]-F[1, 1])/2) && issquarefree((F[2, 1]+F[1, 1])/2), print1(k, ", "))))
%Y A364029 Cf. A046388, A198512, A364028.
%K A364029 nonn
%O A364029 1,1
%A A364029 _Hugo Pfoertner_, Jul 01 2023