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A059054 Integers which can be written as (b^k+1)/(b+1) for positive integers b and k.

%I A059054 #17 Oct 30 2017 04:32:08
%S A059054 1,3,7,11,13,21,31,43,57,61,73,91,111,133,157,171,183,205,211,241,273,
%T A059054 307,343,381,421,463,507,521,547,553,601,651,683,703,757,813,871,931,
%U A059054 993,1057,1111,1123,1191,1261,1333,1407,1483,1561,1641,1723,1807,1893
%N A059054 Integers which can be written as (b^k+1)/(b+1) for positive integers b and k.
%C A059054 It seems that all values are odd. For (b^k+1)/(b+1) to be an integer, it seems k must be odd. 2=(0^0+1)/(0+1) has been excluded since neither b nor k would be positive.
%C A059054 When k is a composite, a(n) is a composite.
%C A059054 These numbers are in the form of 111...1 (k of 1s) base b. - _Lei Zhou_, Feb 08 2012
%H A059054 H. Dubner and T. Granlund, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.
%e A059054 43 is in the sequence since (2^7+1)/(2+1)=129/3=43; indeed also (7^3+1)/(7+1)=344/8=43.
%t A059054 max = 44; maxdata = (1 + max^3)/(1 + max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 + m^i)/(1 + m); cc <= maxdata, a = Append[a, cc]], {m, 2, max}]; Union[a] (* _Lei Zhou_, Feb 08 2012 *)
%Y A059054 Cf. A007583, A002061, A059055.
%K A059054 nonn
%O A059054 1,2
%A A059054 _Henry Bottomley_, Dec 21 2000