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A050458
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Difference between Sum_{d|n, d == 1 mod 4} d^2 and Sum_{d|n, d == 3 mod 4} d^2.
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1
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1, 1, 8, 1, 26, 8, 48, 1, 73, 26, 120, 8, 170, 48, 208, 1, 290, 73, 360, 26, 384, 120, 528, 8, 651, 170, 656, 48, 842, 208, 960, 1, 960, 290, 1248, 73, 1370, 360, 1360, 26, 1682, 384, 1848, 120, 1898, 528, 2208, 8, 2353, 651, 2320, 170, 2810, 656, 3120, 48, 2880, 842
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| Multiplicative with a(p^e) = 1 if p = 2; ((p^2)^(e+1)-1)/(p^2-1) if p == 1 (mod 4); ((p^2)^(e+1)+(-1)^e)/(p^2+1) if p == 3 (mod 4). - Michael Somos Aug 09 2006
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PROG
| (PARI) {a(n)=if(n<1, 0, abs(sumdiv(n, d, d^2*kronecker(-4, d))))} /* Michael Somos Aug 09 2006 */
(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, if(p%4==1, ((p^2)^(e+1)-1)/(p^2-1), ((p^2)^(e+1)+(-1)^e)/(p^2+1)))))) } /* Michael Somos Aug 09 2006 */
(PARI) {a(n)=if(n<1, 0, polcoeff( sum(k=1, n, x^k/(1+x^(2*k))*(k/2^valuation(k, 2))^2, x*O(x^n)), n))} /* Michael Somos Aug 09 2006 */
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CROSSREFS
| a(n)=|A002173(n)|.
Sequence in context: A019432 A002173 A138505 * A125166 A075155 A075151
Adjacent sequences: A050455 A050456 A050457 * A050459 A050460 A050461
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KEYWORD
| nonn,mult
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 15 2004
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EXTENSIONS
| Edited by Michael Somos, Aug 09 2006
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