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%I #19 Jan 04 2025 23:09:19
%S 2,4,17,130,1283,6889,40037,638521,10126943,186814849
%N a(n) is the smallest k such that tau(k*2^n - 1) is equal to 2^n where tau = A000005.
%e a(1) = 2 because tau(2*2^1 - 1) = tau(4 - 1) = tau(3) = 2 = 2^1;
%e a(2) = 4 because tau(4*2^2 - 1) = tau(16 - 1) = tau(15) = 4 = 2^2.
%t a[n_]:=Module[{k=1},While[DivisorSigma[0,k*2^n-1]!=2^n, k++]; k]; Array[a,8] (* _Stefano Spezia_, Dec 29 2024 *)
%o (PARI) a(n) = my(k=1); while (numdiv(k*2^n - 1) != 2^n, k++); k; \\ _Michel Marcus_, Dec 28 2024
%Y Cf. A000005.
%K nonn,more,new
%O 1,1
%A _Juri-Stepan Gerasimov_, Dec 28 2024
%E a(10) from _Michel Marcus_, Dec 28 2024
%E a(4) = 17 removed by _Vincenzo Librandi_, Dec 31 2024
%E a(5) = 1283 from _Vincenzo Librandi_, Dec 31 2024