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A028982
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Squares and twice squares.
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49
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1, 2, 4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 128, 144, 162, 169, 196, 200, 225, 242, 256, 288, 289, 324, 338, 361, 392, 400, 441, 450, 484, 512, 529, 576, 578, 625, 648, 676, 722, 729, 784, 800, 841, 882, 900, 961, 968, 1024
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OFFSET
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1,2
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COMMENTS
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Numbers n such that sum of divisors of n (A000203) is odd.
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, Jan 27 2003
Pell(n)*sum{k|n} 1/Pell(k) is odd, where Pell(n) is A000129(n). - Paul Barry, Oct 12 2005
Number of odd divisors of n (A001227) is odd. - Vladeta Jovovic, Aug 28 2007
A071324(a(n)) is odd. - Reinhard Zumkeller, Jul 03 2008
Sigma(a(n)) = A000203(a(n)) = A152677(n). [From Jaroslav Krizek, Oct 06 2009]
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REFERENCES
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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.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012
P. De Geest, World!Of Numbers
Eric Weisstein's World of Mathematics, Abundance
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FORMULA
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a(n) is asymptotic to c*n^2 with c = 2/(1+sqrt(2))^2 = 0.3431457.... - Benoit Cloitre, Sep 17 2002
In particular, a(n) = cn^2 + O(n). - Charles R Greathouse IV, Jan 11 2013
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MATHEMATICA
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Take[ Sort[ Flatten[ Table[{n^2, 2n^2}, {n, 35}] ]], 57] (* Robert G. Wilson v, Aug 27 2004 *)
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PROG
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(PARI) list(lim)=vecsort(concat(vector(sqrtint(lim\1), i, i^2), vector(sqrtint(lim\2), i, 2*i^2))) \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
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Complement of A028983.
Characteristic function is A053866.
Odd terms in A178910.
Sequence in context: A036349 A155562 A048715 * A175338 A071601 A114400
Adjacent sequences: A028979 A028980 A028981 * A028983 A028984 A028985
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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