%I
%S 35,55,77,95,115,119,143,155,161,187,203,209,215,221,235,247,253,287,
%T 295,299,319,323,329,335,355,371,377,391,395,403,407,413,415,437,473,
%U 493,497,515,517,527,533,535,551,559,581,583,589,611,623,629,635,649,655,667,689,695,697,707,713,731
%N Semiprimes k = pq with primes p < q such that p1 does not divide q1.
%C The "antiCarmichael semiprimes" defined: semiprimes k such that lpf(k)1 does not divide k1; then also gpf(k)1 does not divide k1.
%C All the terms are odd and indivisible by 3.
%C If k is in the sequence, then gcd(k,b^kb)=1 for some integer b.
%C These numbers are probably all semiprimes in A121707.
%H Robert Israel, <a href="/A319386/b319386.txt">Table of n, a(n) for n = 1..10000</a>
%e 35 = 5*7 is a term since 51 does not divide 71.
%e 35 is a term since lpf(35)1 = 51 does not divide 351.
%p N:= 1000: # for terms <= N
%p P:= select(isprime,{seq(i,i=5..N/5,2)}):
%p S:= {}:
%p for p in P do
%p Qs:= select(q > q > p and q <= N/p and (q1 mod (p1) <> 0), P);
%p S:= S union map(`*`,Qs,p);
%p od:
%p sort(convert(S,list)); # _Robert Israel_, Apr 14 2020
%o (PARI) isok(n) = {if ((bigomega(n) == 2) && (omega(n) == 2), my(p = factor(n)[1, 1], q = factor(n)[2, 1]); (q1) % (p1) != 0;);} \\ _Michel Marcus_, Sep 18 2018
%o (PARI) list(lim)=my(v=List(),s=sqrtint(lim\=1)); forprime(q=7,lim\5, forprime(p=5,min(min(q2,s),lim\q), if((q1)%(p1), listput(v,p*q)))); Set(v) \\ _Charles R Greathouse IV_, Apr 14 2020
%Y Subsequence of A046388.
%Y Complement of A162730 w.r.t. A006881.
%Y Cf. A001358, A121707.
%K nonn
%O 1,1
%A _Thomas Ordowski_, Sep 18 2018
