A066959 a(n) = bigomega(n^n) where bigomega(x) is the number of prime factors in x (counted with multiplicity).

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

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) a(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: A060872 A162775 A363501 * A344368 A342768 A340514

Adjacent sequences: A066956 A066957 A066958 * A066960 A066961 A066962

Keyword

nonn

Author

Benoit Cloitre, Feb 01 2002

Status

approved