OFFSET
1,6
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(n) = Sum_{d1|n, d2|n, d1 < d2} (1 - ceiling((d1+d2)/2) + floor((d1+d2)/2)). - Wesley Ivan Hurt, Oct 06 2020
EXAMPLE
Triangle T(n, k) starts for n > 2:
2,
3,
3,
2, 4,
4,
3, 5, 6,
2, 5, 6;
where T(n, k) = the values of k such that 2k = q + g; q, g are distinct divisors of n.
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Lopatin and Juri-Stepan Gerasimov, May 08 2014
EXTENSIONS
Several incorrect terms corrected, and more terms added by Colin Barker, May 10 2014
STATUS
approved