Search: id:A050468
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%I A050468
%S A050468 1,16,80,256,626,1280,2400,4096,6481,10016,14640,20480,28562,38400,
%T A050468 50080,65536,83522,103696,130320,160256,192000,234240,279840,327680,
%U A050468 391251,456992,524960,614400,707282,801280,923520,1048576,1171200
%N A050468 Sum_{d|n, n/d=1 mod 4} d^4 - Sum_{d|n, n/d=3 mod 4} d^4.
%C A050468 Multiplicative because it is the Dirichlet convolution of A000583 = n^4 
               and A101455 = [1 0 -1 0 1 0 -1 ...], which are both multiplicative. 
               Christian G. Bower (bowerc(AT)usa.net) May 17, 2005.
%C A050468 Called E'_4(n) by Hardy.
%D A050468 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 120.
%D A050468 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his 
               life and work, Chelsea Publishing Company, New York 1959, p. 135 
               section 9.3. MR0106147 (21 #4881)
%F A050468 G.f.: Sum_{n>=1} n^4*x^n/(1+x^(2*n)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 16 2002
%o A050468 (PARI) a(n)=if(n<1, 0, sumdiv(n,d, (n/d%2)*(-1)^((n/d-1)/2)*d^4)) /* 
               Michael Somos Sep 12 2005 */
%Y A050468 Cf. A050469, A050470, A050471.
%Y A050468 Sequence in context: A111732 A008511 A130810 this_sequence A068778 A034570 
               A165963
%Y A050468 Adjacent sequences: A050465 A050466 A050467 this_sequence A050469 A050470 
               A050471
%K A050468 nonn,mult
%O A050468 1,2
%A A050468 N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999

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