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.

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

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