A094502 a(n) = A000203(A046528(n)): sigma of those numbers whose sigma is a power of 2, in order of appearance.

1, 4, 8, 32, 32, 128, 128, 256, 512, 1024, 1024, 4096, 4096, 8192, 16384, 32768, 32768, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576, 1048576, 2097152, 2097152, 4194304, 4194304, 4194304, 4194304, 8388608

Offset: 1

Author

Labos Elemer, Jun 02 2004

Keywords

• nonn

Comments

Observe that certain powers of 2 do not arise as sum of divisors of something: 2,16,64,2048. Are there more? Yes, see A094505 and A078426.

Crossrefs

Cf. A000203, A046528, A078426, A094505.

Programs

Mathematica

{ta=Table[0, {100}], u=1}; Do[If[IntegerQ[Log[2, DivisorSigma[1, n]]], Print[n];ta[[u]]=n;u=u+1], {n, 1, 100000000}] DivisorSigma[1, ta]

PARI

isok(n) = (n==1) || (ispower(sigma(n), , &r) && (r==2));
for(n=1, 1e7, if(isok(n), print1(sigma(n)", "))) \\ Altug Alkan, Nov 01 2015

Formula

a(n) = 2^A048947(n). - R. J. Mathar, Sep 22 2016