A234500 Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
578, 683, 893, 998, 1073, 1208, 1403, 1502, 1523, 1568, 1628, 1658, 1853, 1898, 1943, 1964, 2153, 2195, 2243, 2258, 2321, 2393, 2423, 2468, 2503, 2558, 2594, 2657, 2783, 2828, 2933, 3023, 3053, 3098, 3140, 3203, 3273, 3278, 3350, 3383, 3392, 3518, 3548, 3581
Offset: 1
Examples
578 = (3*5*7*11 + 1)/2.
Programs
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Mathematica
t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*) v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234501 *) (w + 1)/2 (* A234502 *) (* Peter J. C. Moses, Dec 23 2013 *) With[{nn=20},Select[Union[(Times@@#+1)/2&/@Subsets[Prime[Range[2,nn]],{4}]],#<=(105Prime[nn]+1)/2&]] (* Harvey P. Dale, Oct 18 2021 *)
Formula
1 + A234105.