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%I #10 Oct 18 2021 15:41:58
%S 578,683,893,998,1073,1208,1403,1502,1523,1568,1628,1658,1853,1898,
%T 1943,1964,2153,2195,2243,2258,2321,2393,2423,2468,2503,2558,2594,
%U 2657,2783,2828,2933,3023,3053,3098,3140,3203,3273,3278,3350,3383,3392,3518,3548,3581
%N Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
%F 1 + A234105.
%e 578 = (3*5*7*11 + 1)/2.
%t t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*)
%t v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234501 *)
%t (w + 1)/2 (* A234502 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t With[{nn=20},Select[Union[(Times@@#+1)/2&/@Subsets[Prime[Range[2,nn]],{4}]],#<=(105Prime[nn]+1)/2&]] (* _Harvey P. Dale_, Oct 18 2021 *)
%Y Cf. A234099, A234103, A234104.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jan 01 2014