%I A027582
%S A027582 1,1,1,2,2,3,4,4,5,6,7,8,9,10,11,14,15,17,20,21,25,29,31,35,39,43,48,53,
%T A027582 57,62,70,75,82,90,96,106,116,124,135,146,157,170,184,197,211,229,244,
%U A027582 262,282,300,322,346,368,393,420,447,476,508,539,572,611,646,685
%N A027582 Sequence satisfies T(T(a))=a, where T is defined below.
%D A027582 S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A 
               Note on Partition Eigensequences, preprint, Nov 15 1996.
%H A027582 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 A027582 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, May 04 2003.
%e A027582 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 A027582 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 A027582 Cf. A027581=T(a).
%Y A027582 Sequence in context: A011885 A008672 A097923 this_sequence A011880 A029044 
               A029043
%Y A027582 Adjacent sequences: A027579 A027580 A027581 this_sequence A027583 A027584 
               A027585
%K A027582 nonn,easy,eigen
%O A027582 0,4
%A A027582 N. J. A. Sloane (njas(AT)research.att.com).