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A318939 If n=0 then 1 otherwise 48*(1+12*A318935(n))*(sum of cubes of odd divisors of n).

%I A318939 #11 Jul 11 2022 14:21:46
%S A318939 1,624,5232,17472,42096,78624,146496,214656,337008,472368,659232,
%T A318939 831168,1178688,1371552,1799808,2201472,2696304,3066336,3960624,
%U A318939 4280640,5304096,6010368,6969024,7592832,9436224,9828624,11499936,12754560,14481024
%N A318939 If n=0 then 1 otherwise 48*(1+12*A318935(n))*(sum of cubes of odd divisors of n).
%H A318939 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 (10).
%p A318939 with(numtheory);
%p A318939 A007814 := n -> padic[ordp](n, 2):
%p A318939 T:= n -> add(2^(3*m),m=0..A007814(n));
%p A318939 f := proc(n) local t2,i,d;
%p A318939 if n=0 then return(1); fi;
%p A318939 t2:=0; for d in divisors(n) do if (d mod 2) = 1 then t2:=t2+d^3; fi; od:
%p A318939 48*(1+12*T(n))*t2;
%p A318939 end;
%p A318939 [seq(f(n),n=0..50)];
%o A318939 (Python)
%o A318939 from sympy import divisor_sigma
%o A318939 def A318939(n): return 3*(1+12*((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 A318939 Cf. A318935, A318938.
%K A318939 nonn
%O A318939 0,2
%A A318939 _N. J. A. Sloane_, Sep 15 2018