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%I #44 Oct 27 2023 22:09:08
%S 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,
%T 52,81,84,29,90,31,160,66,68,70,144,37,76,78,160,41,126,43,132,135,92,
%U 47,240,98,150,102,156,53,216,110,224,114,116,59,240,61,124,189,384
%N Bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity).
%C 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
%H Alois P. Heinz, <a href="/A066959/b066959.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%F a(n) = n*bigomega(n). - _Vladeta Jovovic_, Jun 24 2004
%F 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
%F 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
%t a[n_] := n*PrimeOmega[n]; Table[a[n], {n, 1, 64}] (* _Jean-François Alcover_, Jun 29 2013, after _Vladeta Jovovic_ *)
%o (PARI) for (n=1, 1000, write("b066959.txt", n, " ", bigomega(n^n)) ) \\ _Harry J. Smith_, Apr 11 2010
%o (PARI) a(n)=n*bigomega(n) \\ _Charles R Greathouse IV_, Jul 13 2015
%Y Cf. A001222.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Feb 01 2002
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