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%I #48 Feb 01 2021 21:17:33
%S 0,0,1,1,1,2,1,3,3,2,1,7,1,2,6,6,1,6,1,7,6,2,1,16,3,2,6,7,1,12,1,10,6,
%T 2,6,18,1,2,6,16,1,12,1,7,15,2,1,29,3,6,6,7,1,12,6,16,6,2,1,34,1,2,15,
%U 15,6,12,1,7,6,12,1,39,1,2,15,7,6,12,1,29
%N Number of integer arithmetic means of 2 distinct divisors of n.
%H Antti Karttunen, <a href="/A241534/b241534.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = Sum_{d1|n, d2|n, d1 < d2} (1 - ceiling((d1+d2)/2) + floor((d1+d2)/2)). - _Wesley Ivan Hurt_, Oct 06 2020
%e Triangle T(n, k) starts for n > 2:
%e 2,
%e 3,
%e 3,
%e 2, 4,
%e 4,
%e 3, 5, 6,
%e 2, 5, 6;
%e where T(n, k) = the values of k such that 2k = q + g; q, g are distinct divisors of n.
%e a(20) = 7 because (1,5), (2,4), (2,10), (2,20), (4,10), (4,20) and (10,20) are the 7 values of (g,q) such that (g+q)/2 is an integer. - _Colin Barker_, May 10 2014
%t Table[Sum[Sum[(1 - Ceiling[(i + k)/2] + Floor[(i + k)/2]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}] (* _Wesley Ivan Hurt_, Oct 06 2020 *)
%o (PARI) a(n) = c=0; fordiv(n, g, fordiv(n, q, if(g<q && (g+q)%2==0, c++))); c \\ _Colin Barker_, May 10 2014
%Y Cf. A027750.
%K nonn
%O 1,6
%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, May 08 2014
%E Several incorrect terms corrected, and more terms added by _Colin Barker_, May 10 2014
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