%I #15 Dec 14 2024 20:30:58
%S 0,1,2,2,2,2,2,2,2,3,2,4,3,2,3,2,3,3,2,4,2,3,3,3,3,3,3,4,2,3,3,4,3,3,
%T 3,3,3,3,3,4,2,2,3,4,3,3,4,4,3,4,3,5,3,3,3,3,3,3,2,5,2,4,4,2,4,3,3,5,
%U 3,3,2,4,4,3,5,4,3,3,2,4,2,3,4,4,4,3,3,4,3,4,3,5,4,4,3,5,3,4,4,3,2,3,3,3,3
%N Number of distinct prime factors of sigma_2(n), where sigma_2(n) = A001157(n).
%H Harry J. Smith, <a href="/A066088/b066088.txt">Table of n, a(n) for n=1..1000</a>
%F a(n) = A001221(A001157(n)).
%e sigma_2(12) = 144 + 36 + 16 + 9 + 4 + 1 = 210, so a(12)=4.
%t PrimeNu[DivisorSigma[2,Range[110]]] (* _Harvey P. Dale_, Feb 23 2015 *)
%o (PARI) a(n) = { omega(sigma(n, 2)) } \\ _Harry J. Smith_, Nov 11 2009
%Y Cf. A001157, A001221.
%K nonn
%O 1,3
%A _Labos Elemer_, Dec 04 2001
%E Offset changed from 0 to 1 by _Harry J. Smith_, Nov 11 2009