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 A037213 Expansion of Sum_{n>=0} n*q^(n^2). 28
 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; text; internal format)
 OFFSET 0,5 COMMENTS Multiplicative with a(p^(2e)) = p^e, a(p^(2e+1)) = 0. - Mitch Harris, Jun 09 2005 a(n) is the square root of n if n is square, zero otherwise. - Carl R. White, May 23 2009 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA Dirichlet generating function: zeta(2*s-1). - Franklin T. Adams-Watters, Sep 11 2005. a(n) = sqrt(n) * floor( cos^2(Pi * sqrt(n)) ). - Carl R. White, May 23 2009 a(n) = A000196(n) * A010052(n). - Reinhard Zumkeller, Jan 27 2010 MATHEMATICA Table[If[IntegerQ[n^(1/2)], n^(1/2), 0], {n, 0, 100}] (* Geoffrey Critzer, Feb 21 2015 *) PROG (Haskell) a037213 n = if n == r ^ 2 then r else 0  where r = a000196 n a037213_list = zipWith (*) a010052_list a000196_list -- Reinhard Zumkeller, Nov 09 2012 CROSSREFS Cf. A000196, A010052. Sequence in context: A112166 A112167 A230571 * A218234 A092197 A213618 Adjacent sequences:  A037210 A037211 A037212 * A037214 A037215 A037216 KEYWORD nonn,mult AUTHOR STATUS approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)