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%I #12 Nov 22 2015 15:25:42
%S 14,15,33,35,46,51,55,62,69,77,87,94,95,115,118,119,123,141,142,143,
%T 145,155,158,159,161,166,177,187,203,205,209,213,214,221,235,249,253,
%U 254,265,267,278,287,295,299,302,303,319,321,323,329,334,335,339,341,355
%N Semiprimes pq such that there is another semiprime rs with (p+1)(q+1)=(r+1)(s+1) and p, q, r, and s distinct primes.
%C Note that for a semiprime p*q, the expression (p+1)*(q+1) is the sum of the divisors (A000203) of p*q. - _Michel Marcus_, Jan 29 2015
%C Subsequence of A162283. - _Gionata Neri_, Nov 20 2015
%H T. D. Noe, <a href="/A180328/b180328.txt">Table of n, a(n) for n=1..1000</a>
%e For pq = 14 = 2*7, the corresponding rs is 15 because (2+1)(7+1) = 24 = (3+1)(5+1).
%t nn=1000; sp=Select[Range[2,3*nn/2], Last/@FactorInteger[ # ]=={1, 1}&]; prods=Table[Times@@(1+First/@FactorInteger[n]), {n,sp}]; dups=Select[Tally[prods], #[[2]]>1&]; goodProds=Sort[Transpose[dups][[1]]]; pos=Select[Range[Length[sp]], sp[[ # ]]<=nn && MemberQ[goodProds, prods[[ # ]]]&]; sp[[pos]]
%Y Cf. A000203, A180329 (odd semiprimes with this property).
%K nonn
%O 1,1
%A _T. D. Noe_, Sep 07 2010
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