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A318938 If n=0 then 1 otherwise 16*(1+22*A318935(n))*(sum of cubes of odd divisors of n).

%I A318938 #8 Jul 11 2022 16:09:49
%S A318938 1,368,3184,10304,25712,46368,89152,126592,205936,278576,401184,
%T A318938 490176,719936,808864,1095296,1298304,1647728,1808352,2410288,2524480,
%U A318938 3239712,3544576,4241088,4477824,5766208,5796368,6998432,7521920,8844928,8975520,11233152,10963456,13182064,13724928,15646176,15950592,19463984
%N A318938 If n=0 then 1 otherwise 16*(1+22*A318935(n))*(sum of cubes of odd divisors of n).
%H A318938 P. J. C. Lamont, <a href="https://doi.org/10.1017/S001309150000420X">The number of Cayley integers of given norm</a>, Proceedings of the Edinburgh Mathematical Society, 25.1 (1982): 101-103. See (7).
%p A318938 with(numtheory);
%p A318938 A007814 := n -> padic[ordp](n, 2):
%p A318938 T:= n -> add(2^(3*m),m=0..A007814(n));
%p A318938 f := proc(n) local t2,i,d;
%p A318938 if n=0 then return(1); fi;
%p A318938 t2:=0; for d in divisors(n) do if (d mod 2) = 1 then t2:=t2+d^3; fi; od:
%p A318938 16*(1+22*T(n))*t2;
%p A318938 end;
%p A318938 [seq(f(k),k=0..50)];
%o A318938 (Python)
%o A318938 from sympy import divisor_sigma
%o A318938 def A318938(n): return (1+22*((1<<(3*(m:=(~n&n-1).bit_length())+3))-1)//7)*divisor_sigma(n>>m,3)<<4 if n else 1 # _Chai Wah Wu_, Jul 11 2022
%Y A318938 Cf. A318935.
%K A318938 nonn
%O A318938 0,2
%A A318938 _N. J. A. Sloane_, Sep 15 2018