A241563 - OEIS

%I #7 Apr 25 2014 21:17:37

%S 0,0,1,3,8,14,25,38,58,83,118,158,210,268,339,417,510,611,728,855,

%T 1001,1158,1337,1529,1745,1973,2227,2495,2789,3098,3436,3792,4180,

%U 4587,5028,5488,5984,6500,7053,7627,8241,8880,9562,10270,11022,11802,12627,13478

%N Number of 3-element subsets of {1,...,n} whose sum has more than 2 divisors.

%C If the constraint on the number of divisors is dropped, one gets A000292 = tetrahedral numbers C(n+2,3) = n*(n+1)*(n+2)/6, which therefore is an upper bound.

%C If the sums are required to have more than 3 divisors, one gets A241564.

%o (PARI) a(n,m=3,d=2)={s=0;u=vector(m,n,1)~;forvec(v=vector(m,i,[1,n]),numdiv(v*u)>d&&s++,2);s}

%K nonn

%O 1,4

%A _M. F. Hasler_, Apr 25 2014