A377634 a(n) is the smallest k such that tau(k*2^n - 1) is equal to 2^n where tau = A000005.
2, 4, 17, 130, 1283, 6889, 40037, 638521, 10126943, 186814849, 2092495862
Offset: 1
Examples
a(1) = 2 because tau(2*2^1 - 1) = tau(4 - 1) = tau(3) = 2 = 2^1; a(2) = 4 because tau(4*2^2 - 1) = tau(16 - 1) = tau(15) = 4 = 2^2.
Programs
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Mathematica
a[n_]:=Module[{k=1},While[DivisorSigma[0,k*2^n-1]!=2^n, k++]; k]; Array[a,8] (* Stefano Spezia, Dec 29 2024 *) -
PARI
a(n) = my(k=1); while (numdiv(k*2^n - 1) != 2^n, k++); k; \\ Michel Marcus, Dec 28 2024
Formula
a(n)*2^n - 1 >= A360438(n). - Daniel Suteu, Jan 07 2025
Extensions
a(10) from Michel Marcus, Dec 28 2024
a(4) = 17 removed by Vincenzo Librandi, Dec 31 2024
a(5) = 1283 from Vincenzo Librandi, Dec 31 2024
a(11) from Daniel Suteu, Jan 07 2025
Comments