%I A100715
%S A100715 6,12,18,20,24,28,30,36,40,42,48,54,56,60,72,80,84,90,96,100,108,112,
%T A100715 120,126,140,144,150,160,162,168,180,192,196,200,210,216,224,240,252
%N A100715 Pseudoperfect (or semiperfect) k-brilliant numbers for some k>1: some 
               set of proper divisors of a(n) sums to a(n) and a(n) = p(1)p(2)...p(m) 
               for primes all with the same number of digits.
%C A100715 Since every multiple of a semiperfect number is semiperfect, there are 
               an infinite number of values in this sequence and also an infinite 
               number of values in the complement (pseudoperfect or semiperfect 
               numbers which are not k-brilliant numbers).
%D A100715 Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, 
               Multiperfect and Hyperperfect Numbers." B2 in Unsolved Problems in 
               Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994.
%D A100715 Roberts, J. The Lure of the Integers. Washington, DC: Math. Assoc. Amer., 
               p. 177, 1992.
%D A100715 Zachariou, A. and Zachariou, E. "Perfect, Semi-Perfect and Ore Numbers." 
               Bull. Soc. Math. Greece (New Ser.) 13, 12-22, 1972.
%H A100715 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SemiperfectNumber.html">Semiperfect Number.</a>
%F A100715 a(n) is an element in the intersection of A005835 and A078972. a(n) in 
               A005835 and a(n) is a semiprime with the same number of digits in 
               each prime factor.
%e A100715 6 = 2 * 3 is 2-brilliant.
%e A100715 12 = 2 * 2 * 3 is 3-brilliant.
%e A100715 18 = 2 * 3 * 3 is 3-brilliant.
%e A100715 20 = 2 * 2 * 5 is 3-brilliant.
%e A100715 24 = 2 * 2 * 2 * 3 is 4-brilliant.
%e A100715 28 = 2 * 2 * 7 is 3-brilliant.
%e A100715 30 = 2 * 3 * 5 is 3-brilliant.
%e A100715 36 = 2 * 2 * 3 * 3 is 4-brilliant.
%e A100715 40 = 2 * 2 * 2 * 5 is 4-brilliant.
%e A100715 264 is not in the sequence because it is pseudoperfect but 264 = 2 * 
               2 * 2 * 3 * 11 and 11 has more digits than 2.
%Y A100715 Cf. A005835, A078972, A001358.
%Y A100715 Sequence in context: A023196 A005835 A007620 this_sequence A094519 A088723 
               A138939
%Y A100715 Adjacent sequences: A100712 A100713 A100714 this_sequence A100716 A100717 
               A100718
%K A100715 easy,nonn
%O A100715 1,1
%A A100715 Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 11 2004