OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Tanay Wakhare, Sums involving the number of distinct prime factors function, arXiv:1604.05671 [math.HO], 2016-2017.
FORMULA
If n is squarefree, then a(n) = omega(n)*2^omega(n). - Wesley Ivan Hurt, Jun 09 2020
Dirichlet g.f.: zeta(s)^2 * (2*P(s) - P(2*s)), where P(s) is the prime zeta function (Wakhare, 2016). - Amiram Eldar, Sep 19 2023
EXAMPLE
a(6) = 8; 6 has four divisors {1,2,3,6} and two distinct prime divisors {2,3}, so a(6) = 4*2 = 8.
a(9) = 3; 9 has three divisors {1,3,9} and 1 distinct prime divisor {3}, so a(9) = 3*1 = 3.
a(12) = 12; 12 has 6 divisors {1,2,3,4,6,12} and 2 distinct prime divisors {2,3}, so a(12) = 6*2 = 12.
MATHEMATICA
Table[DivisorSigma[0, n] PrimeNu[n], {n, 100}]
PROG
(PARI) vector(100, n, numdiv(n)*omega(n)) \\ Michel Marcus, Oct 09 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 08 2014
STATUS
approved