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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A046388, A198512, A364028.

Sequence in context: A290435 A138227 A246157 * A301789 A244166 A301963

Adjacent sequences: A364026 A364027 A364028 * A364030 A364031 A364032

Keyword

nonn

Author

Hugo Pfoertner, Jul 01 2023

Status

approved