Search: id:A028982
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%I A028982
%S A028982 1,2,4,8,9,16,18,25,32,36,49,50,64,72,81,98,100,121,128,144,162,169,
%T A028982 196,200,225,242,256,288,289,324,338,361,392,400,441,450,484,512,
%U A028982 529,576,578,625,648,676,722,729,784,800,841,882,900,961,968,1024
%N A028982 Union of nonzero squares and twice squares.
%C A028982 Numbers n such that sum of divisors of n (A000203) is odd.
%C A028982 Also the numbers with an odd number of run sums (trapezoidal arrangements, 
               number of ways of being written as the difference of two triangular 
               numbers). - Ron Knott (maths(AT)ronknott.com), Jan 27 2003
%C A028982 Pell(n)*sum{k|n} 1/Pell(k) is odd, where Pell(n) is A000129(n). - Paul 
               Barry (pbarry(AT)wit.ie), Oct 12 2005
%C A028982 Number of odd divisors of n (A001227) is odd. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 28 2007
%C A028982 A071324(a(n)) is odd. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 03 2008
%C A028982 Sigma(a(n)) = A000203(a(n)) = A152677(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Oct 06 2009]
%D A028982 John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of 
               plane sublattices by parent Patterson symmetry and colour lattice 
               group type, Acta Cryst. (2009). A65, 156163. [From N. J. A. Sloane, 
               (njas(AT)research.att.com), Feb 23 2009]
%H A028982 T. D. Noe, <a href="b028982.txt">Table of n, a(n) for n=1..1000</a>
%H A028982 P. De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of 
               Numbers</a>
%H A028982 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Abundance.html">Abundance</a>
%F A028982 a(n) is asymptotic to c*n^2 with c = 2/(1+sqrt(2))^2 = 0.3431457.... 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 17 2002
%t A028982 Take[ Sort[ Flatten[ Table[{n^2, 2n^2}, {n, 35}] ]], 57] (from Robert 
               G. Wilson v Aug 27 2004)
%Y A028982 Complement of A028983. Characteristic function is A053866.
%Y A028982 Sequence in context: A048300 A155562 A048715 this_sequence A071601 A114400 
               A023898
%Y A028982 Adjacent sequences: A028979 A028980 A028981 this_sequence A028983 A028984 
               A028985
%K A028982 nonn
%O A028982 1,2
%A A028982 Patrick De Geest (pdg(AT)worldofnumbers.com)

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