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A300794 Least number k that is expressible as the sum of 2 abundant numbers in n ways.

%I A300794 #11 Mar 22 2018 04:03:52
%S A300794 24,36,48,66,60,84,90,96,108,126,120,150,144,174,168,364,180,234,392,
%T A300794 228,216,252,240,294,264,288,330,342,312,300,336,402,390,372,700,396,
%U A300794 360,450,408,432,848,522,456,492,420,558,546,516,594,504,480,552,642,540
%N A300794 Least number k that is expressible as the sum of 2 abundant numbers in n ways.
%H A300794 Paolo P. Lava, <a href="/A300794/b300794.txt">Table of n, a(n) for n = 1..10000</a>
%e A300794 a(1) = 24 = 12 + 12;
%e A300794 a(2) = 36 = 12 + 24 = 18 + 18;
%e A300794 a(3) = 48 = 12 + 36 = 18 + 30 = 24 + 24;
%e A300794 a(4) = 66 = 12 + 54 = 18 + 48 = 24 + 42 = 30 + 36,
%e A300794 etc.
%p A300794 with(numtheory); P:=proc(q) local a, b, i, j, n, v; v:=array(1..10^4);
%p A300794 for n from 1 to 10^4 do v[n]:=0; od; a:=0;
%p A300794 for n from 1 to q do b:=0; for i from 1 to trunc(n/2) do
%p A300794 if sigma(i)>2*i and sigma(n-i)>2*(n-i) then b:=b+1; fi; od;
%p A300794 if b=a+1 then a:=b; print(n); j:=1;
%p A300794 while v[b+j]>0 do a:=b+j; print(v[b+j]); j:=j+1; od; else if b>a+1 then
%p A300794 if v[b]=0 then v[b]:=n; fi; fi; fi; od; end: P(10^6);
%t A300794 a[n_] := Block[{t=0, lim=0, ab={}}, While[t == 0, ab = Join[ab, Select[ Range[lim, lim + 499], DivisorSigma[1, #] > 2 # &]]; t = SelectFirst[ Range[lim, lim + 499], Length[ IntegerPartitions[#, {2}, ab]] == n &, 0]; lim += 500]; t]; Array[a, 54] (* _Giovanni Resta_, Mar 14 2018 *)
%Y A300794 Cf. A005101.
%K A300794 nonn,easy
%O A300794 1,1
%A A300794 _Paolo P. Lava_, Mar 13 2018