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A364029
Odd squarefree semiprimes s = p*q such that (p + q)/2 and (p - q)/2 are squarefree.
1
21, 35, 51, 69, 85, 91, 93, 123, 133, 187, 213, 219, 221, 235, 237, 253, 259, 267, 339, 341, 355, 365, 371, 381, 395, 411, 413, 437, 445, 451, 453, 469, 485, 493, 501, 573, 611, 635, 667, 669, 685, 699, 723, 731, 755, 763, 771, 779, 781, 789, 803, 813, 843, 851, 893, 899
OFFSET
1,1
LINKS
MAPLE
filter:= proc(n) local F, p, q;
F:= ifactors(n)[2];
if nops(F) <> 2 or F[1, 2] <> 1 or F[2, 2] <> 1 then return false fi;
p:= F[1, 1]; q:= F[2, 1];
numtheory:-issqrfree((p+q)/2) and numtheory:-issqrfree(abs(p-q)/2)
end proc:
select(filter, [seq(i, i=1..1000, 2)]); # Robert Israel, Dec 12 2023
MATHEMATICA
okQ[n_] := MatchQ[FactorInteger[n], {{p_, 1}, {q_, 1}} /; SquareFreeQ[(p + q)/2] && SquareFreeQ[(q - p)/2]];
Select[Range[1, 1000, 2], okQ] (* Jean-François Alcover, Jun 04 2024 *)
PROG
(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, ", "))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jul 01 2023
STATUS
approved