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Number of distinct prime factors of sigma_2(n), where sigma_2(n) = A001157(n).
2

%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