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A050469
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Sum_{ d divides n, n/d=1 mod 4} d - Sum_{ d divides n, n/d=3 mod 4} d.
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3
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1, 2, 2, 4, 6, 4, 6, 8, 7, 12, 10, 8, 14, 12, 12, 16, 18, 14, 18, 24, 12, 20, 22, 16, 31, 28, 20, 24, 30, 24, 30, 32, 20, 36, 36, 28, 38, 36, 28, 48, 42, 24, 42, 40, 42, 44, 46, 32, 43, 62, 36, 56, 54, 40, 60, 48, 36, 60, 58, 48, 62, 60, 42, 64, 84, 40
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OFFSET
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1,2
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COMMENTS
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Multiplicative with a(p^e)=p^e if p=2, (p^(e+1)-1)/(p-1) if p==1 (mod 4), else (p^(e+1)+(-1)^e)/(p+1). - Michael Somos May 02 2005
Multiplicative because it is the Dirichlet convolution of A000027 = n and A101455 = [1 0 -1 0 1 0 -1 ...], which are both multiplicative. Christian G. Bower May 17, 2005.
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LINKS
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Table of n, a(n) for n=1..66.
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FORMULA
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G.f.: Sum_{n>=1} n*x^n/(1+x^(2*n)). - Vladeta Jovovic, Oct 16 2002
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PROG
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d*((n/d%4==1)-(n/d%4==3))))
(PARI) {a(n)=local(A, p, e); if(n<2, n==1, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, p^e, if(p%4==1, (p^(e+1)-1)/(p-1), (p^(e+1)+(-1)^e)/(p+1)))))) } /* Michael Somos May 02 2005 */
(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, n, k*x^k/(1+x^(2*k)), x*O(x^n)), n))
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CROSSREFS
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Cf. A050470, A050471, A050468.
Sequence in context: A051495 A073256 A166362 * A085730 A219741 A210603
Adjacent sequences: A050466 A050467 A050468 * A050470 A050471 A050472
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane, Dec 23 1999
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STATUS
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approved
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