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%I #5 Mar 30 2012 17:22:56
%S 33,35,51,55,69,77,87,95,115,119,123,141,143,155,159,161,177,187,203,
%T 205,209,213,221,235,249,253,267,287,295,299,303,319,321,323,329,335,
%U 339,341,355,371,391,393,395,407,413,415,437,445,447,451,473,485,493
%N Odd semiprimes pq such that there is another odd semiprime rs with (p+1)(q+1)=(r+1)(s+1) and p, q, r, and s distinct primes.
%C These numbers are related to amicable pairs of the form (G * pq, G * rs), where G is coprime to pq and rs. The interesting case of G=2^n is shown in A180330.
%H T. D. Noe, <a href="/A180329/b180329.txt">Table of n, a(n) for n=1..1000</a>
%e For pq = 33 = 3*11, the corresponding rs is 35 because (3+1)(11+1) = 48 = (5+1)(7+1).
%t nn=1000; sp=Select[Range[3,4*nn/3,2], 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. A180328 (all semiprimes with this property)
%K nonn
%O 1,1
%A _T. D. Noe_, Sep 07 2010
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