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A037213
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Expansion of sum(n*q^(n^2), n=0..inf).
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6
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0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Multiplicative with a(p^(2e)) = p^e, a(p^(2e+1)) = 0. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 09, 2005.
a(n) is the square root of n if n is square, zero otherwise [From Carl R. White (oeisfan(AT)phodd.net), May 23 2009]
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FORMULA
| Dirichlet generating function: zeta(2s-1). - Franklin T. Adams-Watters, Sep 11 2005.
a(n) = sqrt(n) * floor( cos^2(pi * sqrt(n)) ) [From Carl R. White (oeisfan(AT)phodd.net), May 23 2009]
a(n) = A000196(n)*A010052(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 27 2010]
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CROSSREFS
| Sequence in context: A174469 A112166 A112167 * A092197 A083804 A028597
Adjacent sequences: A037210 A037211 A037212 * A037214 A037215 A037216
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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