This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111303 #10 Dec 16 2021 10:38:44 %S A111303 1,3,15,63,255,65535,4294967295 %N A111303 Numbers n such that 2^tau(n) = n + 1 (where tau(n) = number of divisors of n). %C A111303 It is clear that n+1 must be a power of 2. Hence n=2^k-1 for some k. Found k=1, 2, 4, 6, 8, 16, 32. No other k<150. - _T. D. Noe_, Nov 04 2005 %F A111303 Note that this is different from the sequence A019434 - 2. %t A111303 Select[Range[10^6], 2^DivisorSigma[0, # ] == # + 1 &] %t A111303 2^Select[Range[150], DivisorSigma[0, 2^#-1]==#&] - 1 (Noe) %o A111303 (Python) %o A111303 from sympy import divisor_count as tau %o A111303 def afind(klimit, kstart=1): %o A111303 for k in range(kstart, klimit+1): %o A111303 m = 2**k - 1 %o A111303 if 2**tau(m) == m + 1: print(m, end=", ") %o A111303 afind(klimit=100) # _Michael S. Branicky_, Dec 16 2021 %Y A111303 Cf. A046801 (number of divisors of 2^n-1), A019434. %K A111303 nonn,hard,more %O A111303 1,2 %A A111303 _Joseph L. Pe_, Nov 02 2005 %E A111303 One more term from _T. D. Noe_, Nov 04 2005