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

1, 624, 5232, 17472, 42096, 78624, 146496, 214656, 337008, 472368, 659232, 831168, 1178688, 1371552, 1799808, 2201472, 2696304, 3066336, 3960624, 4280640, 5304096, 6010368, 6969024, 7592832, 9436224, 9828624, 11499936, 12754560, 14481024

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 (10).

Crossrefs

Cf. A318935, A318938.

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:
48*(1+12*T(n))*t2;
end;
[seq(f(n),n=0..50)];

Python

from sympy import divisor_sigma
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