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
Keywords
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).
Programs
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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)];
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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