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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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 *) -
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, ", "))))