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A175397 Numbers such that both arithmetic means of distinct and all prime factors are not integers.

%I A175397 #12 Nov 11 2024 07:50:12
%S A175397 1,6,10,12,14,18,22,24,26,28,30,34,36,38,40,46,48,52,54,56,58,62,66,
%T A175397 70,72,74,76,80,82,86,88,90,94,96,98,100,102,104,106,108,118,120,122,
%U A175397 124,130,132,134,136,138,142,144,146,148,150,152,154,158,160,162,165,166,172,174,176,178,182,184
%N A175397 Numbers such that both arithmetic means of distinct and all prime factors are not integers.
%C A175397 Contains all even semiprimes. - _Robert Israel_, Nov 10 2024
%H A175397 Robert Israel, <a href="/A175397/b175397.txt">Table of n, a(n) for n = 1..10000</a>
%e A175397 For a(13) = 36: 36 = 2^2*3^3; both (2+2+3+3)/4 and (2+3)/2 are not integers.
%p A175397 filter:= proc(n) local F,t,m;
%p A175397   F:= ifactors(n)[2]; m:= nops(F);
%p A175397   not (add(t[1],t=F)/m)::integer and not (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer
%p A175397 end proc:
%p A175397 filter(1):= true:
%p A175397 select(filter, [$1..1000]); # _Robert Israel_, Nov 10 2024
%Y A175397 Subsequence of A176552, A175352 and A176587. Complement of A175418. Cf. A174894.
%K A175397 nonn
%O A175397 1,2
%A A175397 _Jaroslav Krizek_, May 01 2010
%E A175397 a(27) corrected, and more terms from _Robert Israel_, Nov 10 2024