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%I #10 Dec 05 2013 19:56:47
%S 3,8,9,32,64,81,128,216,512,1024,1728,2048,4096,6561,7776,8192,13824,
%T 16384,27000,32768,46656,110592,131072,216000,248832,262144,279936,
%U 373248,524288,884736,1048576,1728000,2097152,2985984,4194304,5832000
%N Least number n with a given prime signature such that all numbers >= n with this prime signature are one less than a composite number.
%C This is to categorize prime signatures such that p^a*q^b*r^c ... +1 is composite, p,q,r are arbitrarily chosen primes. Example: Perfect odd powers + 1 is always composite. Are there other examples? Exceptions like 3 and 5 are to be ignored.
%e 8 = 2^3 is a member as 8 has a prime signature p^3 and all numbers of the form p^3+1 are composite.
%e 9 is also a member though 2^2+1 = 5 is a prime but for all odd primes p^2+1 is even.
%e 216 = 2^3*3^3 is a member because p^3*q^3+1 is always divisible by pq+1.
%Y Cf. A093438.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Apr 01 2004
%E More terms from _David Wasserman_, Sep 12 2006