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

Author

Benoit Cloitre, Feb 01 2002

Keywords

• nonn

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)

Crossrefs

Cf. A001222.

Programs

Mathematica

a[n_] := n*PrimeOmega[n]; Table[a[n], {n, 1, 64}] (* Jean-François Alcover, Jun 29 2013, after Vladeta Jovovic *)

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

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