login
The number of divisors of 2*n^2.
3

%I #13 Mar 21 2023 12:31:15

%S 2,4,6,6,6,12,6,8,10,12,6,18,6,12,18,10,6,20,6,18,18,12,6,24,10,12,14,

%T 18,6,36,6,12,18,12,18,30,6,12,18,24,6,36,6,18,30,12,6,30,10,20,18,18,

%U 6,28,18,24,18,12,6,54,6,12,30,14,18,36,6,18,18,36,6,40,6,12,30,18,18,36,6,30

%N The number of divisors of 2*n^2.

%H Project Euler, <a href="https://projecteuler.net/problem=735">Problem 735. Divisors of 2n^2</a>

%F a(n) = A000005(2*n^2) = 2*A078644(n).

%F a(n) = 2*A048691(n) if n odd, = 2*(1+A007814(n)) *A275367(n) if n even.

%p A361689 := proc(n)

%p numtheory[tau](2*n^2) ;

%p end proc:

%p seq(A361689(n),n=1..80) ;

%o (PARI) a(n) = numdiv(2*n^2); \\ _Michel Marcus_, Mar 21 2023

%Y Cf. A000005, A078644, A048691, A007814, A275367.

%K nonn,easy

%O 1,1

%A _R. J. Mathar_, Mar 20 2023