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%I #18 Sep 05 2017 06:10:42
%S 1,2,2,2,8,2,2,8,2,2,8,2,2,8,2,21,5,6,6,15,3,6,8,6,2,10,12,6,12,2,10,
%T 22,8,6,34,6,6,22,8,6,8,2,2,6,8,8,2,6,15,31,6,2,6,8,6,2,2,6,10,2,6,6,
%U 15,13,6,2,6,8,2,8,6,10,6,10,8,8,6,8,6,10,8,2,2,10,2,10,6,2,38,10,6,10,8,10,8
%N a(1)=1. a(n) = the smallest positive integer such that d(a(n)) = d(Sum_{k=1..n} a(k)), where d(m) = the number of divisors of m.
%C Sum_{k=1..n} a(k) = A160690(n).
%C d(a(n)) = d(A160690(n)) = A160691(n).
%H Michel Marcus, <a href="/A160689/b160689.txt">Table of n, a(n) for n = 1..5000</a>
%t a[1] = 1; a[n_] := a[n] = (s = Sum[a[k],{k,n-1}]; For[m = 1, DivisorSigma[0, m] != DivisorSigma[0, s + m], m++]; m); Table[a[n], {n, 95}] (* _Farideh Firoozbakht_, May 28 2009 *)
%o (PARI) lista(nn) = {k = 1; print1(k, ", "); s = k; for (n=2, nn, k = 1; while(numdiv(k) != numdiv(k+s), k++); print1(k, ", "); s += k;);} \\ _Michel Marcus_, Sep 04 2017
%Y Cf. A160690, A160691.
%K nonn
%O 1,2
%A _Leroy Quet_, May 24 2009
%E More terms from _Farideh Firoozbakht_, May 28 2009
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