A078426 Numbers k such that there is no solution to the equation sigma(x) = 2^k, where sigma(x) denotes the sum of the divisors of x.

1, 4, 6, 11, 470, 475, 477, 480, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 522, 525, 527, 532, 1077, 1082

Offset: 1

Author

Shyam Sunder Gupta, Dec 29 2002

Keywords

• nonn

Comments

Numbers that are not a sum of distinct Mersenne exponents (A000043). - Vladeta Jovovic, Jan 01 2003

Because there is a large gap between the 31st and 32nd Mersenne exponents, all k between 704338 and 756839 are in this sequence. - T. D. Noe, Oct 12 2006

A000203(A180162(a(n))) = 6^a(n), for n > 1. - Walter Kehowski, Aug 16 2010

Using all known Mersenne exponents, there are exactly 52935 terms in this sequence. When a new Mersenne prime (with exponent q) is found, there will be no new terms if the sum of the previous Mersenne exponents (A109472) is greater than q - 22.

Examples

			a(2)=4 because no positive integer value of x can satisfy sigma(x) = 2^4 = 16.
		

References

• S. Kravitz, "Beware of the Fifth", Solution to Problem 2309, Journal of Recreational Mathematics, 29(1):76 Baywood NY 1998.

Links

• T. D. Noe, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000203, A007369, A046528, A063883, A180221 (complement).

Programs

Mathematica

e={2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253, 4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091, 756839,859433,1257787,1398269}; u={0}; Do[u=Union[u, u+e[[k]]], {k,Length[e]}]; Complement[Range[e[[-1]]], u]

Extensions

More terms from Vladeta Jovovic, Jan 01 2003

Edited by N. J. A. Sloane, Aug 23 2010

Edited by Max Alekseyev, Jan 24 2014