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%I #19 Mar 23 2017 21:22:49
%S 1,2,6,5,67,11,637,12,348,47,57913,26,472366,463,26105,15,42488697,
%T 118,344373650,136,2089071,2496,30991547417,7,332851440,93936,3467844,
%U 590,22845074981535,31,183014339639657,13,13947373787
%N a(n) = the smallest positive integer not yet occurring such that the number of divisors of Sum_{k=1..n} a(k) is exactly n.
%C It seems likely that this is a permutation of the positive integers. Is it?
%F Sum_{k=1..n} a(k) = A175351(n).
%e a(4) = k where sigma(a(1) + a(2) + a(3) + k) = sigma(9 + k) = 4. The next number larger than 9 having four divisors is 10. This would give k = 1, which is in the sequence. The next number larger than 10 having four divisors is 14. This would give k = 14 - 9 = 5, which isn't already in the sequence. Therefore, a(4) = 5. - _David A. Corneth_, Mar 08 2017
%t a[1]=1;a[n_]:=a[n]=Module[{an=First[Complement[Range[n],a/@Range[n-1]]]},
%t While[DivisorSigma[0,Sum[a[i],{i,n-1}]+an]!=n||MemberQ[a/@Range[n-1],an],an++];
%t an];a/@Range[16] (* _Ivan N. Ianakiev_, Mar 08 2017 *)
%Y Cf. A001055, A175351.
%K nonn
%O 1,2
%A _Leroy Quet_, Apr 19 2010
%E More terms from _Farideh Firoozbakht_, Mar 20 2010
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