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%I #26 Feb 22 2016 04:51:16
%S 3,9,20,27,60,81,112,180,243,336,400,540,729,1008,1200,1620,2187,2240,
%T 2816,3024,3600,4860,6561,6720,8000,8448,9072,10800,12544,13312,14580,
%U 19683,20160,24000,25344,27216,32400,37632,39936,43740,44800,56320,59049,60480
%N The arithmetic mean of the prime factors (with multiplicity) of n is 3.
%H Reinhard Zumkeller and Donovan Johnson, <a href="/A200612/b200612.txt">Table of n, a(n) for n = 1..500</a> (first 150 terms from Reinhard Zumkeller)
%F A001414(a(n)) mod A001222(a(n)) = 0 and A001414(a(n))/A001222(a(n)) = 3. [_Reinhard Zumkeller_, Nov 20 2011]
%e 20 is in the sequence because 20 = 2*2*5 and (2+2+5)/3 = 9/3 = 3.
%p for i from 2 to 35000 do: a:=ifactors(i): s:=sum((a[2][j][1]*a[2][j][2]),j=1..nops(a[2])): t:=sum((a[2][j][2]),j=1..nops(a[2])): if s/t=3 then print(i); fi od:
%t Select[Range[61000],Mean[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[ #]]]==3&] (* _Harvey P. Dale_, Nov 08 2013 *)
%o (Haskell)
%o a200612 n = a200612_list !! (n-1)
%o a200612_list = filter f [2..] where
%o f x = r == 0 && x' == 3 where (x',r) = divMod (a001414 x) (a001222 x)
%o -- _Reinhard Zumkeller_, Nov 20 2011
%o (PARI) isok(n) = my(f = factor(n)); (sum(k=1, #f~, f[k,1]*f[k,2]) / vecsum(f[,2])) == 3; \\ _Michel Marcus_, Feb 22 2016
%Y Subsequence of A078175.
%K nonn
%O 1,1
%A _Jeffrey Burch_, Nov 19 2011
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