|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|