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%I #12 Nov 16 2024 16:07:21
%S 2,3,4,5,7,8,9,11,13,15,16,17,19,21,23,25,27,29,31,32,33,35,37,39,41,
%T 42,43,47,49,51,53,55,57,59,61,64,65,67,69,71,73,77,78,79,81,83,85,87,
%U 89,91,93,95,97,101
%N Numbers such that the arithmetic mean of their distinct prime factors and the arithmetic mean of all of their prime factors are both integers.
%C Subsequence of A078174 and A078175.
%C Complement of A176552. [From _Jaroslav Krizek_, Apr 21 2010]
%H Harvey P. Dale, <a href="/A174894/b174894.txt">Table of n, a(n) for n = 1..1000</a>
%e For a(11) = 16: 16 = 2^4; both (2+2+2+2)/4 and 2/1 are integers.
%t mdmaQ[n_]:=With[{fi=FactorInteger[n]},AllTrue[{Mean[Flatten[Table[#[[1]],#[[2]]]&/@fi]],Mean[fi[[;;,1]]]},IntegerQ]]; Select[Range[ 2,110],mdmaQ] (* _Harvey P. Dale_, Nov 16 2024 *)
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Apr 01 2010
%E Definition clarified by _Harvey P. Dale_, Nov 16 2024