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A361687 The number of divisors of 2*n^2 which are <=n.

%I A361687 #13 Mar 21 2023 12:31:34
%S A361687 1,2,3,3,3,5,3,4,5,6,3,8,3,6,8,5,3,9,3,8,9,6,3,11,5,6,7,8,3,16,3,6,9,
%T A361687 6,8,14,3,6,9,11,3,16,3,9,13,6,3,14,5,10,9,9,3,13,9,11,9,6,3,24,3,6,
%U A361687 14,7,9,16,3,9,9,17,3,18,3,6,14,9,8,17,3,14,9,6,3,24,9,6,9,11
%N A361687 The number of divisors of 2*n^2 which are <=n.
%H A361687 Project Euler, <a href="https://projecteuler.net/problem=735">Problem 735. Divisors of 2n^2</a>
%e A361687 a(15)=8 because the divisors of 2*15^2=450 which are <=15 are 1, 2, 3, 5, 6, 9, 10 and 15.
%p A361687 A361687 := proc(n)
%p A361687     local a,d;
%p A361687     a := 0 ;
%p A361687     for d in numtheory[divisors](2*n^2) do
%p A361687         if d <= n then
%p A361687             a := a+1 ;
%p A361687         end if;
%p A361687     end do:
%p A361687     a ;
%p A361687 end proc:
%p A361687 seq(A361687(n),n=1..120) ;
%o A361687 (PARI) a(n) = sumdiv(2*n^2, d, d <= n); \\ _Michel Marcus_, Mar 21 2023
%Y A361687 Cf. A361689.
%K A361687 nonn
%O A361687 1,2
%A A361687 _R. J. Mathar_, Mar 20 2023