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
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 01 2002
STATUS
approved