%I
%S 4,8,9,25,27,35,39,55,65,119,125,185,203,219,235,237,289,305,319,341,
%T 415,417,437,515,535,597,649,655,671,685,749,755,905,935,959,979,989,
%U 1003,1043,1079,1111,1119,1165,1227,1247,1285,1299,1315,1343,1355,1465,1469,1565,1649,1681,1735,1739,1829
%N Composite numbers n such that n+1+d is prime for all nontrivial divisors d which divide n.
%C 4 and 8 are the only even numbers.
%C Numbers in the sequence which are not semiprimes: 8, 27, 125, 935, 1859, 2849 etc.  R. J. Mathar, Jan 06 2009
%F {n: n+1+d in A000040 for all 1<d<n with dn}.
%e For n=8, the nontrivial divisors are 2 and 4 and (8+1)+2 = 11 and (8+1)+4 = 13 are both prime.
%e For 35 the nontrivial divisors are 5 and 7. With (35+1) + 5=41 and (35+1) + 7 = 43, both sums are primes.
%K easy,nonn
%O 1,1
%A _J. M. Bergot_, Dec 23 2008
%E Added 4, replaced 121 by 125, extended, simplified definition, added nonsemiprime examples. _R. J. Mathar_, Jan 06 2009
