

A078426


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


12



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
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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 n 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



