A175397 - OEIS

%I #12 Nov 11 2024 07:50:12

%S 1,6,10,12,14,18,22,24,26,28,30,34,36,38,40,46,48,52,54,56,58,62,66,

%T 70,72,74,76,80,82,86,88,90,94,96,98,100,102,104,106,108,118,120,122,

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

%C Contains all even semiprimes. - _Robert Israel_, Nov 10 2024

%H Robert Israel, <a href="/A175397/b175397.txt">Table of n, a(n) for n = 1..10000</a>

%e For a(13) = 36: 36 = 2^2*3^3; both (2+2+3+3)/4 and (2+3)/2 are not integers.

%p filter:= proc(n) local F,t,m;

%p   F:= ifactors(n)[2]; m:= nops(F);

%p   not (add(t[1],t=F)/m)::integer and not (add(t[1]*t[2],t=F)/add(t[2],t=F))::integer

%p end proc:

%p filter(1):= true:

%p select(filter, [$1..1000]); # _Robert Israel_, Nov 10 2024

%Y Subsequence of A176552, A175352 and A176587. Complement of A175418. Cf. A174894.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 01 2010

%E a(27) corrected, and more terms from _Robert Israel_, Nov 10 2024