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A088595 Numbers n such that (A006530(n) + A020639(n))/2 is an integer, divides n and it is not a power of prime number: it has at least 2 distinct prime factors. Special terms of A088948.

%I A088595 #28 Nov 26 2016 16:15:59
%S A088595 105,231,315,525,627,693,735,897,935,945,1155,1575,1581,1617,1729,
%T A088595 1881,2079,2205,2465,2541,2625,2691,2835,2967,3135,3465,3525,3675,
%U A088595 4123,4301,4389,4485,4675,4715,4725,4743,4851,5145,5487,5643,5775,6237,6279,6545
%N A088595 Numbers n such that (A006530(n) + A020639(n))/2 is an integer, divides n and it is not a power of prime number: it has at least 2 distinct prime factors. Special terms of A088948.
%C A088595 Every number of the sequence has at least three different prime factors. Also, the sequence is infinite (it contains all numbers of the form 3^a*5^b*7^c with a,b,c>0). - _Emmanuel Vantieghem_, Nov 21 2016
%H A088595 Robert Israel, <a href="/A088595/b088595.txt">Table of n, a(n) for n = 1..10000</a>
%e A088595 n = 315 = 3*3*5*7 is not a power of a prime, has 3 prime factors and (3+5)/2=7 divides n.
%p A088595 filter:= proc(n) local F;
%p A088595   F:= numtheory:-factorset(n);
%p A088595   nops(F) > 2 and n mod (min(F)+max(F))/2 = 0
%p A088595 end proc:
%p A088595 select(filter, [seq(i,i=1..10^4,2)]); # _Robert Israel_, Nov 21 2016
%t A088595 Rest@ Select[Range@ 6600, Function[n, And[IntegerQ@ #, Divisible[n, #], ! PrimePowerQ@ n] &[(#[[-1, 1]] + #[[1, 1]])/2] &@ FactorInteger@ n]] (* _Michael De Vlieger_, Nov 24 2016 *)
%Y A088595 Cf. A006530, A020639, A088948, A088949.
%K A088595 nonn
%O A088595 1,1
%A A088595 _Labos Elemer_, Nov 20 2003