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

1, 368, 3184, 10304, 25712, 46368, 89152, 126592, 205936, 278576, 401184, 490176, 719936, 808864, 1095296, 1298304, 1647728, 1808352, 2410288, 2524480, 3239712, 3544576, 4241088, 4477824, 5766208, 5796368, 6998432, 7521920, 8844928, 8975520, 11233152, 10963456, 13182064, 13724928, 15646176, 15950592, 19463984

Offset: 0

Author

N. J. A. Sloane, Sep 15 2018

Keywords

• nonn

Links

• P. J. C. Lamont, The number of Cayley integers of given norm, Proceedings of the Edinburgh Mathematical Society, 25.1 (1982): 101-103. See (7).

Crossrefs

Cf. A318935.

Programs

Maple

with(numtheory);
A007814 := n -> padic[ordp](n, 2):
T:= n -> add(2^(3*m),m=0..A007814(n));
f := proc(n) local t2,i,d;
if n=0 then return(1); fi;
t2:=0; for d in divisors(n) do if (d mod 2) = 1 then t2:=t2+d^3; fi; od:
16*(1+22*T(n))*t2;
end;
[seq(f(k),k=0..50)];

Python

from sympy import divisor_sigma
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