Search: id:A050999
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%I A050999
%S A050999 1,1,10,1,26,10,50,1,91,26,122,10,170,50,260,1,290,91,362,26,500,122,
%T A050999 530,10,651,170,820,50,842,260,962,1,1220,290,1300,91,1370,362,1700,26,
%U A050999 1682,500,1850,122,2366,530,2210,10,2451,651
%N A050999 Sum of squares of odd divisors of n.
%H A050999 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               OddDivisorFunction.html">Link to a section of The World of Mathematics.</
               a>
%F A050999 Multiplicative with a(p^e) = 1 if p = 2, (p^(2e+2)-1)/(p^2-1) if p > 
               2. a(n) = 1/2*Sum_{d|n} ((1-(-1)^d)*d^2. a(2n)=sigma_2(2n)-4*sigma_2(n), 
               a(2n+1)=sigma_2(2n+1), where sigma_2(n) is sum of squares of divisors 
               of n (A001157). More generally, if b(n, k) is sum of k-th powers 
               of odd divisors of n then b(2n, k) = sigma_k(2n)-2^k*sigma_k(n), 
               b(2n+1, k) =sigma_k(2n+1). b(n, k) is multiplicative with a(p^e) 
               = 1 if p = 2, (p^(ke+k)-1)/(p^k-1) if p > 2. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Sep 10 2001
%F A050999 G.f. for b(n, k): Sum_{m>0} m^k*x^m*(1-(2^k-1)*x^m)/(1-x^(2*m)). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Oct 19 2002
%Y A050999 Cf. A051000, A051001, A051002, A000593, A001227, A000203, A001157-A001160, 
               A013954-A013972.
%Y A050999 Sequence in context: A040109 A036188 A013617 this_sequence A070246 A085044 
               A059022
%Y A050999 Adjacent sequences: A050996 A050997 A050998 this_sequence A051000 A051001 
               A051002
%K A050999 nonn,mult
%O A050999 1,3
%A A050999 Eric Weisstein (eric(AT)weisstein.com)

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