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A175418 Complement of A175397, where A175397 = numbers such that both arithmetic means of distinct and all prime factors are not integers.

%I A175418 #15 Nov 11 2024 07:26:39
%S A175418 2,3,4,5,7,8,9,11,13,15,16,17,19,20,21,23,25,27,29,31,32,33,35,37,39,
%T A175418 41,42,43,44,45,47,49,50,51,53,55,57,59,60,61,63,64,65,67,68,69,71,73,
%U A175418 75,77,78,79,81,83,84,85,87,89,91,92,93,95,97,99
%N A175418 Complement of A175397, where A175397 = numbers such that both arithmetic means of distinct and all prime factors are not integers.
%C A175418 For these numbers hold that both arithmetic means of distinct and all prime factors are integers or only one of these means is an integer.
%C A175418 Includes all prime powers and odd semiprimes. - _Robert Israel_, Nov 10 2024
%H A175418 Robert Israel, <a href="/A175418/b175418.txt">Table of n, a(n) for n = 1..10000</a>
%p A175418 filter:= proc(n) local F,t;
%p A175418   F:= ifactors(n)[2];
%p A175418   (add(t[1],t=F)/nops(F))::integer or (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
%p A175418 end proc:
%p A175418 select(filter, [$2..100]); # _Robert Israel_, Nov 10 2024
%Y A175418 Cf. A174894, A176552, A175352, A175397, A176587.
%K A175418 nonn
%O A175418 1,1
%A A175418 _Jaroslav Krizek_, May 09 2010
%E A175418 a(49) corrected by _Robert Israel_, Nov 10 2024