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A361689 The number of divisors of 2*n^2.

%I A361689 #13 Mar 21 2023 12:31:15
%S A361689 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 A361689 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 A361689 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 A361689 The number of divisors of 2*n^2.
%H A361689 Project Euler, <a href="https://projecteuler.net/problem=735">Problem 735. Divisors of 2n^2</a>
%F A361689 a(n) = A000005(2*n^2) = 2*A078644(n).
%F A361689 a(n) = 2*A048691(n) if n odd, = 2*(1+A007814(n)) *A275367(n) if n even.
%p A361689 A361689 := proc(n)
%p A361689         numtheory[tau](2*n^2) ;
%p A361689 end proc:
%p A361689 seq(A361689(n),n=1..80) ;
%o A361689 (PARI) a(n) = numdiv(2*n^2); \\ _Michel Marcus_, Mar 21 2023
%Y A361689 Cf. A000005, A078644, A048691, A007814, A275367.
%K A361689 nonn,easy
%O A361689 1,1
%A A361689 _R. J. Mathar_, Mar 20 2023