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.

Showing 1-3 of 3 results.

A246456 a(n) = sigma(n + sigma(n)).

Original entry on oeis.org

3, 6, 8, 12, 12, 39, 24, 24, 36, 56, 24, 90, 40, 60, 56, 48, 48, 80, 56, 96, 54, 90, 48, 224, 120, 126, 68, 224, 60, 216, 104, 120, 121, 180, 84, 128, 124, 171, 120, 252, 84, 288, 120, 255, 168, 180, 120, 308, 162, 168, 168, 372, 108, 360, 128, 372, 138, 266
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Examples

			For n = 6; a(n) = sigma(6 + sigma(6)) = sigma(18) = 39.

Crossrefs

Cf. A000203, A246909, A246907 (numbers n such that a(n) = 3n), A246915 (numbers n such that a(n) = a(n+1)).
Cf. Sequences of numbers n such that a(n) = k*sigma(n):
A246857 (k=2), A246910 (k=3), A246911 (k=4), A246912 (k=5), A246913 (k=6).

Programs

  • Magma
    [SumOfDivisors(n+SumOfDivisors(n)):n in[1..1000]]
  • PARI
    vector(100,n,sigma(n+sigma(n))) \\ Derek Orr, Sep 07 2014

A246909 a(n) = the smallest numbers k such that sigma(k+sigma(k)) = n* sigma(k) or -1 if no solution exists or has been found for n.

Original entry on oeis.org

-1, 2, 1, 28, 15456, 831376
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Comments

a(7) > 10^7 or -1.

Examples

			Sequence of numbers k such that sigma(k+sigma(k)) = n* sigma(k)  for 1 <= n <= 6:
n = 2: 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, … (A246857).
n = 3: 1, 7, 26, 30, 42, 54, 69, 78, 84, 94, 102, 103, 114, … (A246910).
n = 4: 28, 66, 348, 496, 840, 920, 1320, 1416, 1602, 1770, … (A246911).
n = 5: 15456, 16920, 48576, 59520, 107160, 153360, 232596, … (A246912).
n = 6: 831376, 3944688, 16956576, 17843616, … (A246913).

Crossrefs

Cf. A000203, A246910, A246911, A246912, A246913, A246914.

Programs

A246858 Composite numbers k such that sigma(k + sigma(k)) = 2*sigma(k).

Original entry on oeis.org

329, 413, 623, 869, 979, 1819, 2585, 3107, 3173, 3197, 3887, 4235, 4997, 5771, 6149, 6187, 6443, 7409, 8399, 8759, 14429, 15323, 18515, 19019, 21181, 21413, 23989, 26491, 29749, 30355, 31043, 32623, 34009, 34177, 39737, 47321, 47845, 51389, 53311, 56419
Offset: 1

Views

Author

Jaroslav Krizek, Sep 05 2014

Keywords

Comments

Complement of A005384 (Sophie Germain primes) with respect to A246857.

Examples

			Number 329 (with sigma(329) = 384) is in sequence because sigma(329 + sigma(329)) = sigma(713) = 768 = 2*384.

Crossrefs

Cf. A074400, A246456.
Cf. A005384, A246858.

Programs

  • Magma
    [n:n in[1..1000] | SumOfDivisors(n+SumOfDivisors(n)) eq 2*SumOfDivisors(n) and not IsPrime(n)]
  • Mathematica
    Select[Range[57000], And[CompositeQ[#], DivisorSigma[1, # + DivisorSigma[1, #]] == 2 DivisorSigma[1, #]] &] (* Michael De Vlieger, Aug 05 2021 *)
  • PARI
    lista(nn) = {forcomposite(n=2, nn, if (sigma(n+sigma(n)) == 2*sigma(n), print1(n, ", ")););} \\ Michel Marcus, Sep 05 2014
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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