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

1,2

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.

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

Example

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

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]

Crossrefs

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

Sequence in context: A105308 A116983 A196271 * A212558 A293836 A278252

Adjacent sequences: A078423 A078424 A078425 * A078427 A078428 A078429

Keyword

nonn

Author

Shyam Sunder Gupta, Dec 29 2002

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

Status

approved