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

1,2

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.

Links

Table of n, a(n) for n=1..34.

Formula

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

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]

Prog

(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

Crossrefs

Cf. A000203, A046528, A078426, A094505.

Sequence in context: A149091 A149092 A188117 * A162459 A129195 A180098

Adjacent sequences: A094499 A094500 A094501 * A094503 A094504 A094505

Keyword

nonn

Author

Labos Elemer, Jun 02 2004

Status

approved