A377634 - OEIS

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, 8167862431, 317808279653, 19868058417139, 372463979178257, 8397590340722566, 247135209858703658, 5936944176786966589, 461253291943122843287, 14056815667499681190676, 84041646512308648720838, 12266961234721756656121669

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OFFSET

1,1

LINKS

David A. Corneth, Table of n, a(n) for n = 1..27

FORMULA

a(n)*2^n - 1 >= A360438(n). - Daniel Suteu, Jan 07 2025

EXAMPLE

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.

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 *)