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!)
 A066959 Bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity). 13
 0, 2, 3, 8, 5, 12, 7, 24, 18, 20, 11, 36, 13, 28, 30, 64, 17, 54, 19, 60, 42, 44, 23, 96, 50, 52, 81, 84, 29, 90, 31, 160, 66, 68, 70, 144, 37, 76, 78, 160, 41, 126, 43, 132, 135, 92, 47, 240, 98, 150, 102, 156, 53, 216, 110, 224, 114, 116, 59, 240, 61, 124, 189, 384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, a variant of the arithmetic derivative A003415, with f(p)=p (instead of f(p)=1), i.e., f(Product_i p_i^e_i) = Sum_i e_i * Product_i p_i^e_i. - M. F. Hasler, Jul 13 2015 LINKS Harry J. Smith and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith) FORMULA a(n) = n*bigomega(n). - Vladeta Jovovic, Jun 24 2004 Defined by a(p) = p for p prime and a(mn) = a(m)*n + m*a(n). An analogous sequence with a(p) = 1 is A003415. - David W. Wilson, Mar 02 2011 G.f.: x*f'(x), where f(x) = Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). - Ilya Gutkovskiy, Apr 10 2017 MATHEMATICA a[n_] := n*PrimeOmega[n]; Table[a[n], {n, 1, 64}] (* Jean-François Alcover, Jun 29 2013, after Vladeta Jovovic *) PROG (PARI) for (n=1, 1000, write("b066959.txt", n, " ", bigomega(n^n)) ) \\ Harry J. Smith, Apr 11 2010 (PARI) a(n)=n*bigomega(n) \\ Charles R Greathouse IV, Jul 13 2015 CROSSREFS Cf. A001222. Sequence in context: A296070 A060872 A162775 * A344368 A342768 A340514 Adjacent sequences:  A066956 A066957 A066958 * A066960 A066961 A066962 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 01 2002 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 July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)