

A066959


Bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity).


4



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
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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}] (* JeanFrançois 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 * A086471 A249154 A262351
Adjacent sequences: A066956 A066957 A066958 * A066960 A066961 A066962


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Feb 01 2002


STATUS

approved



