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

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, 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, 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

Offset: 1

Author

R. J. Mathar, Mar 20 2023

Keywords

• nonn

Examples

			a(15)=8 because the divisors of 2*15^2=450 which are <=15 are 1, 2, 3, 5, 6, 9, 10 and 15.
		

Links

• Project Euler, Problem 735. Divisors of 2n^2

Crossrefs

Cf. A361689.

Programs

Maple

A361687 := proc(n)
    local a,d;
    a := 0 ;
    for d in numtheory[divisors](2*n^2) do
        if d <= n then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A361687(n),n=1..120) ;

PARI

a(n) = sumdiv(2*n^2, d, d <= n); \\ Michel Marcus, Mar 21 2023