The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A074816 a(n) = 3^A001221(n) = 3^omega(n). 7
 1, 3, 3, 3, 3, 9, 3, 3, 3, 9, 3, 9, 3, 9, 9, 3, 3, 9, 3, 9, 9, 9, 3, 9, 3, 9, 3, 9, 3, 27, 3, 3, 9, 9, 9, 9, 3, 9, 9, 9, 3, 27, 3, 9, 9, 9, 3, 9, 3, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 27, 3, 9, 9, 3, 9, 27, 3, 9, 9, 27, 3, 9, 3, 9, 9, 9, 9, 27, 3, 9, 3, 9, 3, 27, 9, 9, 9, 9, 3, 27, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Old name was: a(n) = sum(d|n, tau(d)*mu(d)^2 ). Terms are powers of 3. The inverse Mobius transform of A074823, as the Dirichlet g.f. is product_{primes p} (1+2*p^(-s)) and the Dirichlet g.f. of A074816 is product_{primes p} (1+2*p^(-s))/(1-p^(-s)). - R. J. Mathar, Feb 09 2011 If n is squarefree, then a(n) = #{(x, y) : x, y positive integers, lcm (x, y) = n}. See Crandall & Pomerance. - Michel Marcus, Mar 23 2016 REFERENCES R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.3 p. 108. LINKS R. Zumkeller, Table = of n, a(n) for n = 1..10000 FORMULA a(n) = 3^m if n is divisible by m distinct primes. i.e. a(n)=3 if n is in A000961; a(n)=9 if n is in A007774 ... a(n) = 3^A001221(n) = 3^omega(n). Multiplicative with a(p^e)=3. - Vladeta Jovovic, Sep 09 2002. a(n) = tau_3(rad(n)) = A007425(A007947(n)). - Enrique Pérez Herrero, Jun 24 2010 a(n) = abs(sum(d|n, A000005(d^3)*mu(d))). - Enrique Pérez Herrero, Jun 28 2010 a(n) = Sum_{d|n, gcd(d, n/d) = 1} 2^omega(d). - Amiram Eldar, May 29 2020 MATHEMATICA A074816[n_]:=3^PrimeNu[n]; (* Enrique Pérez Herrero, Jun 28 2010 *) PROG (PARI) a(n) = 3^omega(n); \\ Michel Marcus, Mar 23 2016 CROSSREFS Cf. A001221, A034444, A124508. Sequence in context: A333793 A007428 A184099 * A203564 A111575 A161836 Adjacent sequences:  A074813 A074814 A074815 * A074817 A074818 A074819 KEYWORD nonn,mult AUTHOR Benoit Cloitre, Sep 08 2002 EXTENSIONS Simpler definition at the suggestion of Michel Marcus. - N. J. A. Sloane, Mar 25 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 31 12:41 EDT 2020. Contains 338101 sequences. (Running on oeis4.)