

A062011


a(n) = 2*tau(n) = 2*A000005(n).


20



2, 4, 4, 6, 4, 8, 4, 8, 6, 8, 4, 12, 4, 8, 8, 10, 4, 12, 4, 12, 8, 8, 4, 16, 6, 8, 8, 12, 4, 16, 4, 12, 8, 8, 8, 18, 4, 8, 8, 16, 4, 16, 4, 12, 12, 8, 4, 20, 6, 12, 8, 12, 4, 16, 8, 16, 8, 8, 4, 24, 4, 8, 12, 14, 8, 16, 4, 12, 8, 16, 4, 24, 4, 8, 12, 12, 8, 16, 4, 20, 10, 8, 4, 24, 8, 8, 8, 16
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OFFSET

1,1


COMMENTS

Old definition was "Number of cyclic subgroups of the group C_n X C_2 (where C_n is the cyclic group with n elements)."
More generally, the number of cyclic subgroups of the group C_n X C_m is Sum_{in, jm} phi(i)*phi(j)/phi(lcm(i,j)), where phi=Euler totient function, cf. A000010.  Vladeta Jovovic, Jul 15 2001
Number of divisors of p*n, where p is any prime not dividing n.  Reinhard Zumkeller, May 17 2006
If p(x) is a polynomial with integer coefficients, and if r is an integer zero of p(x), then r is a divisor of the constant term c_0 of p(x). Under this theorem, p(x) can have a(c_0) possible integer roots.
a(n) is the number of integer divisors of n, while A000005(n) is the number of positive divisors. (End)
Number of solutions to the Diophantine equation i*j = n*i + j.  Robert G. Wilson v, Apr 10 2019
a(n) is also the number of times n appears in the triangle A333119, or equivalently, the number of positive integer solutions of the equation A333119(x, y) = n for y < x.  Stefano Spezia, Oct 05 2022


LINKS



FORMULA

L.g.f.: log(Product_{k>=1} (1  x^k)^(2/k)) = Sum_{n>=1} a(n)*x^n/n.  Ilya Gutkovskiy, Mar 18 2018


MATHEMATICA



PROG

(PARI) for (n=1, 1000, write("b062011.txt", n, " ", 2*numdiv(n))) \\ Harry J. Smith, Jul 29 2009


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Jul 12 2001


EXTENSIONS

Edited by N. J. A. Sloane, Sep 20 2018, replacing old definition (which was of course correct) with a simple formula.


STATUS

approved



