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%I #12 Jan 02 2023 12:30:50
%S 0,0,1,2,6,11,22,35,55,78,110,145,192,245,312,386,476,572,684,804,943,
%T 1091,1261,1442,1647,1864,2108,2366,2651,2951,3281,3629,4010,4410,
%U 4845,5299,5790,6301,6850,7420,8031,8665,9342,10043,10788,11559,12375,13215
%N Number of 3-element subsets of {1,...,n} whose sum has more than 3 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 subsets with more than 2 divisors are counted, one gets A241563.
%H Robert Israel, <a href="/A241564/b241564.txt">Table of n, a(n) for n = 1..5000</a>
%H W. E. Clark in reply to A. Hatzipolakis, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-April/012875.html">A generalization</a>, SeqFan list, Apr 24 2014
%p N:= 100: # for a(1)..a(N)
%p t:= 0: R:= NULL:
%p for n from 1 to N do
%p v:= select(s -> numtheory:-tau(s+n)>3, [$2..2*n-3]);
%p t:= t + add(floor((s-1)/2) - max(0,s-n) , s = v);
%p R:= R, t;
%p od:
%p R; # _Robert Israel_, Jan 04 2021
%o (PARI) a(n,m=3,d=3)={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
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