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A078426
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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.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers that are not a sum of distinct Mersenne primes (A000043). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 01 2003
Comment from T. D. Noe, Oct 12 2006: Because there is a large gap between the 31st and 32nd Mersenne primes, all n between 704338 and 756839 are in this sequence.
A000203(A180162(a(n))) = 6^a(n), for n>1. - Walter A. Kehowski (walter.kehowski(AT)gcmail.maricopa.edu), 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.
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REFERENCES
| S. Kravitz, "Beware of the Fifth", Solution to Problem 2309, Journal of Recreational Mathematics, 29(1):76 Baywood NY 1998.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..350
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EXAMPLE
| a(2)=4 because no positive integer value of x can satisfy sigma(x)=2^4=16.
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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]
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CROSSREFS
| Cf. A063883, A046528.
Sequence in context: A105308 A116983 A196271 * A152678 A110758 A189765
Adjacent sequences: A078423 A078424 A078425 * A078427 A078428 A078429
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KEYWORD
| nonn
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AUTHOR
| Shyam Sunder Gupta (guptass(AT)rediffmail.com), Dec 29 2002
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 01 2003
Edited by N. J. A. Sloane, Aug 23 2010
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