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Search: id:A028982
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| A028982 |
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Union of nonzero squares and twice squares. |
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40
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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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 (maths(AT)ronknott.com), Jan 27 2003
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
Number of odd divisors of n (A001227) is odd. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 28 2007
A071324(a(n)) is odd. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 03 2008
Sigma(a(n)) = A000203(a(n)) = A152677(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 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. [From N. J. A. Sloane, (njas(AT)research.att.com), Feb 23 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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 (benoit7848c(AT)orange.fr), Sep 17 2002
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MATHEMATICA
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Take[ Sort[ Flatten[ Table[{n^2, 2n^2}, {n, 35}] ]], 57] (from Robert G. Wilson v Aug 27 2004)
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CROSSREFS
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Complement of A028983. Characteristic function is A053866.
Sequence in context: A048300 A155562 A048715 this_sequence A071601 A114400 A023898
Adjacent sequences: A028979 A028980 A028981 this_sequence A028983 A028984 A028985
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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