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A365473 Odd semiprimes p*q such that A000120(p)*A000120(q) = A000120(p*q).

%I A365473 #14 Sep 07 2023 12:47:47
%S A365473 15,51,85,95,111,119,123,187,219,221,335,365,411,447,485,511,629,655,
%T A365473 685,697,771,831,879,959,965,1011,1139,1241,1285,1405,1535,1563,1649,
%U A365473 1731,1779,1799,1923,1983,2005,2019,2031,2045,2227,2605,2735,2815,2827,2885,3099,3183,3279,3281,3291,3327
%N A365473 Odd semiprimes p*q such that A000120(p)*A000120(q) = A000120(p*q).
%C A365473 If p is an odd prime < 2^m and A365475(m) exists, then p * A365475(m) is a term.  Thus, if A365475 is infinite, this sequence contains infinitely many multiples of every odd prime.
%H A365473 Robert Israel, <a href="/A365473/b365473.txt">Table of n, a(n) for n = 1..7230</a>
%e A365473 a(3) = 85 is a term because 85 = 5 * 17 is an odd semiprime with A000120(5) * A000120(17) = 2 * 2 = 4 = A000120(85).
%p A365473 g:= proc(n) convert(convert(n,base,2),`+`) end proc:
%p A365473 N:= 10^4: # for terms <= N
%p A365473 S:= NULL: p:= 2:
%p A365473 while 3*p <= N do
%p A365473   p:= nextprime(p);
%p A365473   t:= g(p);
%p A365473   q:= 2:
%p A365473   do
%p A365473     q:= nextprime(q);
%p A365473     if q = p or q*p > N then break fi;
%p A365473     if g(q)*t = g(p*q) then S:= S, p*q fi;
%p A365473 od od:
%p A365473 sort([S]);
%Y A365473 Cf. A000120, A365475.
%Y A365473 Intersection of A001358 and A235040, and intersection of A001358 and A365451.
%K A365473 nonn,base
%O A365473 1,1
%A A365473 _Robert Israel_, Sep 04 2023