Search: id:A050456
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%I A050456
%S A050456 1,1,80,1,626,80,2400,1,6481,626,14640,80,28562,2400,50080,1,83522,
%T A050456 6481,130320,626,192000,14640,279840,80,391251,28562,524960,2400,
%U A050456 707282,50080,923520,1,1171200,83522,1502400,6481,1874162,130320
%V A050456 1,1,-80,1,626,-80,-2400,1,6481,626,-14640,-80,28562,-2400,-50080,1,83522,
%W A050456 6481,-130320,626,192000,-14640,-279840,-80,391251,28562,-524960,-2400,
%X A050456 707282,-50080,-923520,1,1171200,83522,-1502400,6481,1874162,-130320
%N A050456 Sum_{d|n, d=1 mod 4} d^4 - Sum_{d|n, d=3 mod 4} d^4.
%C A050456 Multiplicative because it is the Inverse Moebius transform of [1 0 -3^4 
               0 5^4 0 -7^4 ...], which is multiplicative. Christian G. Bower (bowerc(AT)usa.net) 
               May 18, 2005.
%C A050456 Called E_4(n) by Hardy.
%D A050456 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 120.
%D A050456 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 A050456 G.f.: Sum_{k>0} (-1)^(k-1) (2k-1)^4*x^(2k-1)/(1-x^(2k-1)).
%o A050456 (PARI) a(n)=if(n<1, 0, sumdiv(n,d, (d%2)*(-1)^((d-1)/2)*d^4)) /* Michael 
               Somos Sep 12 2005 */
%Y A050456 Sequence in context: A128472 A093404 A031136 this_sequence A107930 A033400 
               A126783
%Y A050456 Adjacent sequences: A050453 A050454 A050455 this_sequence A050457 A050458 
               A050459
%K A050456 sign,mult
%O A050456 1,3
%A A050456 N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999

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