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

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, 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, 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

Offset: 1

Author

R. J. Mathar, Mar 20 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

Maple

A361689 := proc(n)
        numtheory[tau](2*n^2) ;
end proc:
seq(A361689(n),n=1..80) ;

PARI

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

Formula

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

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