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A282534 Integers that are powers of Mersenne numbers A000225 (i.e., of the form (2^n - 1)^m).

%I A282534 #31 Mar 08 2017 11:55:39
%S A282534 1,3,7,9,15,27,31,49,63,81,127,225,243,255,343,511,729,961,1023,2047,
%T A282534 2187,2401,3375,3969,4095,6561,8191,16129,16383,16807,19683,29791,
%U A282534 32767,50625,59049,65025,65535,117649,131071,177147,250047,261121,262143,524287,531441,759375
%N A282534 Integers that are powers of Mersenne numbers A000225 (i.e., of the form (2^n - 1)^m).
%C A282534 The cardinality of the set of subsets in a multiset excluding empty subsets.
%H A282534 Giovanni Resta, <a href="/A282534/b282534.txt">Table of n, a(n) for n = 1..10000</a>
%e A282534 3 = (2^2-1), 7 = (2^3-1), 9 = (2^2-1)^2, 81 = (2^2-1)^4, 1070599167 = (2^10-1)^3.
%t A282534 mx = 10^6; Union@ Flatten@ {1, #^Range[Log[#, mx]] & /@ (2^ Range[2, Log2@ mx] -1)} (* _Giovanni Resta_, Mar 08 2017 *)
%o A282534 (PARI) ismn(n) = n++; n == 2^valuation(n,2);
%o A282534 isok(n) = ismn(n) || (ispower(n,,&m) && ismn(m)); \\ _Michel Marcus_, Feb 18 2017
%Y A282534 Cf. A000225, A056652.
%K A282534 nonn
%O A282534 1,2
%A A282534 _Andrew Ivashenko_, Feb 18 2017
%E A282534 More terms from _Michel Marcus_, Feb 18 2017