Search: id:A109386
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%I A109386
%S A109386 1,3,7,7,11,21,15,15,34,33,23,49,27,45,77,31,35,102,39,77,105,69,47,105,
%T A109386 86,81,142,105,59,231,63,63,161,105,165,238,75,117,189,165,83,315,87,
%U A109386 161,374,141,95,217,162,258,245,189,107,426,253,225,273,177,119,539,123
%N A109386 G.f. is the logarithm of the g.f. of A107742: Sum_{n>=1} (a(n)/n)*x^n 
               = Log( Sum_{n>=0} A107742(n)*x^n ).
%F A109386 a(n) = Sum_{d|n} d * Sum_{m|d} (m mod 2). G.f.: Sum_{n>=1} a(n)/n*x^n 
               = Sum_{j>=1} Sum_{i>=1} log(1+x^(i*j)).
%F A109386 G.f.: Sum_{n>0} n*A000005(n)*x^n/(1+x^n). a(n) = A060640(n) if n is odd, 
               else a(n) = A060640(n)-2*A060640(n/2). Multiplicative with a(2^e) 
               = 2^(e+1)-1 and a(p^e) = (p^(e+2)*(e+1)-p^(e+1)*(e+2)+1)/(p-1)^2 
               for p>2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 05 2005
%F A109386 Also g.f.: Sum_{n>0} n*A001227(n)*x^n/(1-x^n). a(n)=Sum_{d|n} d*A001227(d). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 05 2005
%F A109386 Also a(n) = Sum_{d|n} d*A000593(n/d). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 05 2005
%F A109386 A107742(n) = (1/n)*Sum_{k=1..n} a(k)*A107742(n-k). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jul 05 2005
%o A109386 (PARI) a(n)=sumdiv(n,d,d*sumdiv(d,m,m%2))
%o A109386 (PARI from Joerg Arndt (arndt(AT)jjj.de), May 03, 2008)
%o A109386 N=17; default(seriesprecision,N); x=z+O(z^(N+1))
%o A109386 c=sum(j=1,N,j*x^j);
%o A109386 t=1/prod(j=0,N, eta(x^(2*j+1)))
%o A109386 t=log(t)
%o A109386 t=serconvol(t,c)
%o A109386 Vec(t)
%Y A109386 Cf. A107742.
%Y A109386 Sequence in context: A140382 A080457 A119644 this_sequence A024612 A073881 
               A137315
%Y A109386 Adjacent sequences: A109383 A109384 A109385 this_sequence A109387 A109388 
               A109389
%K A109386 nonn,mult
%O A109386 1,2
%A A109386 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 26 2005

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