A035198 - OEIS

%I #14 Sep 29 2020 20:51:29

%S 1,9,17,25,41,73,81,89,97,113,121,137,153,169,193,225,233,241,257,281,

%T 289,313,337,353,361,369,401,409,425,433,449,457,521,569,577,593,601,

%U 617,625,641,657,673,697,729,761,769,801,809,841,857,873,881,929,937

%N From a Dirichlet series.

%C Contribution from _R. J. Mathar_, Jul 16 2010: (Start)

%C The Dirichlet function is (z_1(s))^2*z_3(2*s)*z_5(2*s) = 1+ 2/9^s+4/17^s+2/25^s+4/41^s+..,

%C where z_1(s) = prod_{p in A007519} Zeta(s,p) = 1+2/17^s+2/41^s+2/73^s+ ...(see A004625),

%C z_3(s) = prod_{p in A007520} Zeta(s,p) = 1+2/3^s+2/9^s+2/11^s+2/19^s+2/27^s+4/33^s+..,

%C z_5(s) = prod_{p in A007521} Zeta(s,p) = 1+2/5^s+2/13^s+...+4/65^s+2/101^s+..., Zeta(s,p)=(1+p^(-s))/(1-p^(-s)). (End)

%H P. A. B. Pleasants, M. Baake, J. Roth, <a href="http://dx.doi.org/10.1063/1.531424">Planar coincidences for N-fold symmetry</a> J. Math. Phys. 37 (1996) 1029.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _R. J. Mathar_, Jul 16 2010

%E More terms from _Sean A. Irvine_, Sep 29 2020