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Search: id:A050468
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| A050468 |
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Sum_{d|n, n/d=1 mod 4} d^4 - Sum_{d|n, n/d=3 mod 4} d^4. |
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+0
5
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| 1, 16, 80, 256, 626, 1280, 2400, 4096, 6481, 10016, 14640, 20480, 28562, 38400, 50080, 65536, 83522, 103696, 130320, 160256, 192000, 234240, 279840, 327680, 391251, 456992, 524960, 614400, 707282, 801280, 923520, 1048576, 1171200
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
Called E'_4(n) by Hardy.
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REFERENCES
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E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 120.
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)
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FORMULA
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G.f.: Sum_{n>=1} n^4*x^n/(1+x^(2*n)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 16 2002
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PROGRAM
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(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 */
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CROSSREFS
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Cf. A050469, A050470, A050471.
Sequence in context: A111732 A008511 A130810 this_sequence A068778 A034570 A069840
Adjacent sequences: A050465 A050466 A050467 this_sequence A050469 A050470 A050471
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KEYWORD
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nonn,mult
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AUTHOR
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njas, Dec 23 1999
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