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Search: id:A050456
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| A050456 |
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Sum_{d|n, d=1 mod 4} d^4 - Sum_{d|n, d=3 mod 4} d^4. |
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+0
2
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| 1, 1, -80, 1, 626, -80, -2400, 1, 6481, 626, -14640, -80, 28562, -2400, -50080, 1, 83522, 6481, -130320, 626, 192000, -14640, -279840, -80, 391251, 28562, -524960, -2400, 707282, -50080, -923520, 1, 1171200, 83522, -1502400, 6481, 1874162, -130320
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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_{k>0} (-1)^(k-1) (2k-1)^4*x^(2k-1)/(1-x^(2k-1)).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (d%2)*(-1)^((d-1)/2)*d^4)) /* Michael Somos Sep 12 2005 */
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CROSSREFS
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Sequence in context: A128472 A093404 A031136 this_sequence A107930 A033400 A126783
Adjacent sequences: A050453 A050454 A050455 this_sequence A050457 A050458 A050459
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KEYWORD
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sign,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
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