cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Labos Elemer, Jun 02 2004

Keywords

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

A247473 Numbers of the form 2^k (k>=0) that are a sum of divisors of n for some n.

Original entry on oeis.org

1, 4, 8, 32, 128, 256, 512, 1024, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368
Offset: 1

Views

Author

Jaroslav Krizek, Feb 27 2015

Keywords

Comments

Set of values A094502(n) = sigma(A046528(n)) in increasing order.
Complement of A094505 with respect to A000079 (powers of 2).
Corresponding values of numbers k>0 are in A180221.

Examples

			32 = 2^5 is in sequence because there are numbers n = 21 and 31 with sigma(n) = 32.

Crossrefs

Cf. A000079, A000203, A046528, A078426, A094502, A094505, A180221.

Programs

  • Magma
    Set(Sort([SumOfDivisors(n): n in [A046528(n)]]))
  • Magma
    Set(Sort([SumOfDivisors(n): n in[1..10000], k in [0..100] | SumOfDivisors(n) eq 2^k]))
  • Magma
    [1] cat [2^n: n in[A180221(n)]]

Formula

a(1) = 1, for n>=2, a(n) = 2^A180221(n-1).
Showing 1-2 of 2 results.

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