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A094518 Number of pairs (x,y) of divisors of n with x such that also x+y is a divisor of n.

%I A094518 #13 Sep 11 2018 17:02:49
%S A094518 0,0,0,0,0,1,0,0,0,0,0,3,0,0,0,0,0,2,0,1,0,0,0,5,0,0,0,0,0,4,0,0,0,0,
%T A094518 0,6,0,0,0,2,0,3,0,0,0,0,0,7,0,0,0,0,0,3,0,1,0,0,0,12,0,0,0,0,0,2,0,0,
%U A094518 0,1,0,11,0,0,0,0,0,2,0,3,0,0,0,9,0,0,0,0,0,9,0,0,0,0,0,9,0,0,0,2,0,2
%N A094518 Number of pairs (x,y) of divisors of n with x<y such that also x+y is a divisor of n.
%C A094518 a(A094519(n)) > 0, a(A094520(n)) = 0.
%C A094518 a(A097370(n)) = n and a(m) <> n for m < A097370(n).
%H A094518 Antti Karttunen, <a href="/A094518/b094518.txt">Table of n, a(n) for n = 1..65537</a>
%e A094518 n=30 with divisor set {1,2,3,5,6,10,15,30}: a(30)=4, as 1<2 & 3=1+2, 1<5 & 6=1+5, 2<3 & 5=2+3 and 5<10 & 15=5+10.
%t A094518 Table[Count[Subsets[#, {2}], _?(Mod[n, Total@ #] == 0 &)] &@ Divisors@ n, {n, 102}] (* _Michael De Vlieger_, Sep 10 2018 *)
%o A094518 (PARI) A094518(n) = if(1==n,0,my(d=divisors(n),c=0); for(i=1,(#d-1),for(j=(i+1),#d,if(!(n%(d[i]+d[j])),c++))); (c)); \\ _Antti Karttunen_, Sep 10 2018
%Y A094518 Cf. A091009.
%K A094518 nonn
%O A094518 1,12
%A A094518 _Reinhard Zumkeller_, May 06 2004