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%I #18 Jun 22 2024 08:01:55
%S 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,3
%N Number of distinct representations A005244(n) = A005244(i)*A005244(j)-1 with i < j.
%C A139129 gives the smallest terms in A005244 having exactly n representations.
%H Robert Israel, <a href="/A139128/b139128.txt">Table of n, a(n) for n = 1..10000</a> (n = 1 to 500 from R. Zumkeller)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadterSequences.html">Hofstadter Sequences</a>
%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%e A005244(28) = 129: a(28) = #{26*5-1,65*2-1} = 2.
%p R:= [2,3]: count:= 2:
%p for i from 4 while count < 10000 do
%p found:= false;
%p for j from 1 while R[j]^2 < i+1 do
%p if i mod R[j] = R[j]-1 and ListTools:-BinarySearch(R,(i+1)/R[j]) <> 0 then
%p found:= true; break
%p fi
%p od;
%p if found then R:= [op(R),i]; count:= count+1;
%p od:
%p f:= proc(n) local t,i,j,x,L;
%p x:= R[n]+1:
%p L:= R[1..n-1];
%p t:= 0:
%p for i from 1 while R[i]^2 < x do
%p if x mod R[i] = 0 and ListTools:-BinarySearch(L,x/R[i]) <> 0 then t:= t+1 fi
%p od;
%p t
%p end proc:
%p map(f, [$1..10000]); # _Robert Israel_, Jun 21 2024
%K nonn
%O 1,28
%A _Reinhard Zumkeller_, Apr 09 2008
%E a(2) corrected and definition clarified by _Robert Israel_, Jun 21 2024
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