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A283160 Numbers n such that there is exactly one solution to the equation sigma(x)= 2^n, where sigma(x) denotes the sum of the divisors of x. 2
0, 2, 3, 8, 9, 13, 14, 16, 465, 467, 468, 472, 473, 478, 479, 481, 521, 523, 524, 529, 530, 534, 535, 537, 1072, 1074, 1075, 1079, 1080, 1085, 1086, 1088, 1128, 1130, 1131, 1136, 1137, 1141, 1142, 1144, 1744, 1746, 1747, 1751, 1752, 1757, 1758, 1760, 1800, 1802, 1803, 1808, 1809, 1813, 1814 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that there is a unique subset S of the Mersenne exponents A000043 summing to n. - Charles R Greathouse IV, Mar 07 2017

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..168

FORMULA

A283446(a(n)) = 1.

EXAMPLE

8 is in this sequence that k = 217 is the only number having sigma(k) = 2^8.

PROG

(PARI) is(n)=my(N=2^n, s); for(k=1, N, if(sigma(k)==N && s++>1, return(0))); s \\ Charles R Greathouse IV, Mar 07 2017

(PARI) list(lim)=my(v=List(), M=[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, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667], x='x, P); if(lim>M[#M], error("Need more Mersenne exponents to compute further")); M=select(p->p<=lim, M); P=prod(i=1, #M, 1+x^M[i], O(x^(lim\1+1))+1); for(i=0, lim, if(polcoeff(P, i)==1, listput(v, i))); P=0; Vec(v) \\ Charles R Greathouse IV, Mar 07 2017

CROSSREFS

Cf. A000203, A046528, A063883, A078426, A247956.

Sequence in context: A273783 A075190 A224225 * A281148 A284791 A281111

Adjacent sequences:  A283157 A283158 A283159 * A283161 A283162 A283163

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Mar 01 2017

EXTENSIONS

a(9)-a(55) from Charles R Greathouse IV, Mar 07 2017

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)