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A185642 Nearest integer to average of distinct prime factors of n.

%I A185642 #35 Sep 23 2016 14:29:23
%S A185642 2,3,2,5,3,7,2,3,4,11,3,13,5,4,2,17,3,19,4,5,7,23,3,5,8,3,5,29,3,31,2,
%T A185642 7,10,6,3,37,11,8,4,41,4,43,7,4,13,47,3,7,4,10,8,53,3,8,5,11,16,59,3,
%U A185642 61,17,5,2,9,5,67,10,13,5,71,3,73,20,4,11,9,6,79
%N A185642 Nearest integer to average of distinct prime factors of n.
%C A185642 a(n) = n if and only if n is prime.
%H A185642 Harvey P. Dale, <a href="/A185642/b185642.txt">Table of n, a(n) for n = 2..1000</a>
%H A185642 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A185642 a(n) = round(A008472(n)/A001221(n)).
%e A185642 a(12) = 3, since the prime factors of 12 are 2 and 3, the average of 2 and 3 is 2.5, and the nearest integer to 2.5 is 3 (the larger number is chosen when the average is a half-integer).
%t A185642 Table[Floor[Mean[FactorInteger[n][[All,1]]]+1/2],{n,2,80}] (* _Harvey P. Dale_, Sep 23 2016 *)
%o A185642 (PARI) for(n=2, 79, o=omega(n); s=sum(i=1, o, factor(n)[, 1][i]); print1(round(s/o), ", "));
%Y A185642 Cf. A001221, A008472.
%K A185642 nonn
%O A185642 2,1
%A A185642 _Arkadiusz Wesolowski_, Sep 11 2013