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

1, 3, 7, 9, 15, 27, 31, 49, 63, 81, 127, 225, 243, 255, 343, 511, 729, 961, 1023, 2047, 2187, 2401, 3375, 3969, 4095, 6561, 8191, 16129, 16383, 16807, 19683, 29791, 32767, 50625, 59049, 65025, 65535, 117649, 131071, 177147, 250047, 261121, 262143, 524287, 531441, 759375

Offset: 1

Author

Andrew Ivashenko, Feb 18 2017

Keywords

• nonn

Comments

The cardinality of the set of subsets in a multiset excluding empty subsets.

Examples

			3 = (2^2-1), 7 = (2^3-1), 9 = (2^2-1)^2, 81 = (2^2-1)^4, 1070599167 = (2^10-1)^3.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000225, A056652.

Programs

Mathematica

mx = 10^6; Union@ Flatten@ {1, #^Range[Log[#, mx]] & /@ (2^ Range[2, Log2@ mx] -1)} (* Giovanni Resta, Mar 08 2017 *)

PARI

ismn(n) = n++; n == 2^valuation(n,2);
isok(n) = ismn(n) || (ispower(n,,&m) && ismn(m)); \\ Michel Marcus, Feb 18 2017

Extensions

More terms from Michel Marcus, Feb 18 2017