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Search: id:A050457
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| A050457 |
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Sum_{ d divides n, d=1 mod 4} d - Sum_{ d divides n, d=3 mod 4} d. |
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+0
1
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| 1, 1, -2, 1, 6, -2, -6, 1, 7, 6, -10, -2, 14, -6, -12, 1, 18, 7, -18, 6, 12, -10, -22, -2, 31, 14, -20, -6, 30, -12, -30, 1, 20, 18, -36, 7, 38, -18, -28, 6, 42, 12, -42, -10, 42, -22, -46, -2, 43, 31, -36, 14, 54, -20, -60, -6, 36, 30, -58, -12, 62, -30, -42, 1, 84, 20, -66, 18, 44, -36, -70
(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 0 5 0 -7 ...], which is multiplicative. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
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FORMULA
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a(n) is multiplicative with a(p^e)=1 if p=2, a(p^e)=(p^(e+1)-1)/(p-1) if p == 1 (mod 4), a(p^e)=((-p)^(e+1)-1)/(-p-1) if p == 3 (mod 4). - Michael Somos May 29 2005
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PROGRAM
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(PARI) {a(n)=local(A, p, e); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 1, p*=kronecker(-4, p); (p^(e+1)-1)/(p-1)))))} /* Michael Somos May 29 2005 */
(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-4, d)*d))} /* Michael Somos May 29 2005 */
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CROSSREFS
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Sequence in context: A134133 A157392 A134134 this_sequence A076891 A071883 A099304
Adjacent sequences: A050454 A050455 A050456 this_sequence A050458 A050459 A050460
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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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