Search: id:A100546
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%I A100546
%S A100546 2,3,5,7,11,13,17,18,19,23,24,29,30,31,37,41,42,43,47,53,59,61,66,67,71,
%T A100546 73,78,79,83,89,97,101,102,103,107,109,113,114,127,131,137,138,139,149,
%U A100546 151,157,163,167,173,174,179,181,186,191,193,197,199,211,222,223,227
%N A100546 Difference between the smallest semiperimeter (see A063655) and its integer 
               log (A001414) equals 1.
%C A100546 Theorem: Except for 24, the sequence is the union of primes and 6*primes.
%e A100546 Any prime p, since it has semiperimeter p+1 and its integer log is p.
%t A100546 logint = Function[n, Module[{vn}, vn = Transpose[FactorInteger[n]];vn[[1]].vn[[2]] 
               ]]; semiperi = Function[n, Min[Divisors[n] + Reverse[Divisors[n]]]]; 
               sq = {}; Do[If[semiperi[k] == logint[k] + 1, AppendTo[sq, k]], {k, 
               2, 500}]; sq
%Y A100546 Cf. A001414 and A063655.
%Y A100546 Sequence in context: A020625 A033633 A117285 this_sequence A117094 A074721 
               A152073
%Y A100546 Adjacent sequences: A100543 A100544 A100545 this_sequence A100547 A100548 
               A100549
%K A100546 nonn
%O A100546 0,1
%A A100546 Carlos Alves (cjsalves(AT)gmail.com), Dec 31 2004

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