%I A027581
%S A027581 1,1,1,2,2,3,4,5,6,8,10,12,15,17,21,26,30,36,43,49,58,69,79,91,106,122,
%T A027581 140,161,183,209,239,271,308,348,392,444,501,561,630,708,791,884,989,
%U A027581 1101,1225,1365,1516,1681,1863,2062,2282,2522,2782,3069,3381,3719,4092
%N A027581 Sequence satisfies T(T(a))=a, where T is defined below.
%D A027581 S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A 
               Note on Partition Eigensequences, preprint, Nov 15 1996
%H A027581 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/
               0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 
               226-228 (1995), 57-72; erratum 320 (2000), 210.
%F A027581 Define T:a->b by: given a0<=a1<=..., remove duplicates, keep only odd 
               numbers, getting c0<c1<...; define b0, b1, b2, ... by Sum bi*x^i 
               = Product 1/(1-x^ci). - Description corrected by and more terms from 
               Michael Somos, Apr 27 2003.
%e A027581 1+1x+1x^2+2x^3+2x^4+3x^5+4x^6+5x^7+6*x^8+8*x^9+10*x^10+12*x^11+15*x^12+... 
               = 1/((1-x^1)(1-x^3)(1-x^5)(1-x^7)(1-x^9)(1-x^11)(1-x^15)(1-x^17)(1-x^21)...)
%e A027581 1+1x+1x^2+2x^3+2x^4+3x^5+4x^6+4x^7+5*x^8+6*x^9+7*x^10+8*x^11+9*x^12+... 
               = 1/((1-x^1)(1-x^3)(1-x^5)(1-x^15)(1-x^17)(1-x^21)...)
%Y A027581 Cf. A027582=T(a).
%Y A027581 Sequence in context: A083847 A034142 A008675 this_sequence A058706 A034143 
               A034144
%Y A027581 Adjacent sequences: A027578 A027579 A027580 this_sequence A027582 A027583 
               A027584
%K A027581 nonn,easy,eigen
%O A027581 0,4
%A A027581 N. J. A. Sloane (njas(AT)research.att.com).
%E A027581 Description corrected by and more terms from Michael Somos, Apr 27 2003.