A283160 Numbers k such that there is exactly one solution to the equation sigma(x) = 2^k, 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
Keywords
Examples
8 is in this sequence that k = 217 is the only number having sigma(k) = 2^8.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..168
Programs
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Mathematica
With[{e = MersennePrimeExponent[Range[16]]}, Select[Range[0, e[[-1]]], SeriesCoefficient[Series[Product[1 + x^e[[i]], {i, 1, Length[e]}], {x, 0, #}], #] == 1 &]] (* Amiram Eldar, Dec 20 2024 *) -
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
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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
Formula
A063883(a(n)) = 1.
Extensions
a(9)-a(55) from Charles R Greathouse IV, Mar 07 2017
Comments