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 1-4 of 4 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

A246910 Numbers n such that sigma(n+sigma(n)) = 3*sigma(n).

Original entry on oeis.org

1, 7, 26, 30, 42, 54, 69, 78, 84, 94, 102, 103, 114, 138, 140, 174, 222, 258, 354, 364, 474, 476, 498, 520, 532, 534, 582, 618, 644, 650, 762, 764, 812, 834, 847, 894, 978, 1002, 1036, 1038, 1050, 1182, 1185, 1194, 1204, 1214, 1362, 1372, 1398, 1434, 1487
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Comments

A246914 gives the primes in this sequence.

Examples

			Number 26 (with sigma(26) = 42) is in sequence because sigma(26+sigma(26)) = sigma(68) = 126 = 3*42.

Links

Crossrefs

Cf. A000203, A246456, A246909, A246911, A246912, A246913, A246914, A272027.

Programs

  • Magma
    [n:n in[1..10000] | SumOfDivisors(n+SumOfDivisors(n)) eq 3*SumOfDivisors(n)]
  • Maple
    with(numtheory): A246910:=n->`if`(sigma(n+sigma(n)) = 3*sigma(n),n,NULL): seq(A246910(n), n=1..5000); # Wesley Ivan Hurt, Sep 07 2014
  • PARI
    for(n=1,10^4,if(sigma(n+sigma(n))==3*sigma(n),print1(n,", "))) \\ Derek Orr, Sep 07 2014

A246912 Numbers n such that sigma(n+sigma(n)) = 5*sigma(n).

Original entry on oeis.org

15456, 16920, 48576, 59520, 107160, 153360, 232596, 281916, 306720, 332280, 332640, 358560, 360360, 373104, 383400, 514080, 548772, 556920, 788256, 876960, 884520, 930384, 943344, 950040, 955296, 1234464, 1357020, 1396440, 1421280, 1534080, 1539720, 1582866
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Examples

			Number 15456 (with sigma(15456) = 48384) is in sequence because sigma(15456+sigma(15456)) = sigma(63840) = 241920 = 5*48384.

Crossrefs

Cf. A000203, A246456, A246909, A246910, A246911, A246913, A246914, A274535 (5*sigma(n)).

Programs

  • Magma
    [n:n in[1..10^7] | SumOfDivisors(n+SumOfDivisors(n))eq 5*SumOfDivisors(n)]
  • Maple
    with(numtheory): A246912:=n->`if`(sigma(n+sigma(n)) = 5*sigma(n),n,NULL): seq(A246912(n), n=1..10^6); # Wesley Ivan Hurt, Sep 07 2014
  • Mathematica
    Select[Range[16*10^5],DivisorSigma[1,#+DivisorSigma[1,#]] == 5*DivisorSigma[ 1,#]&] (* Harvey P. Dale, Mar 13 2016 *)
  • PARI
    for(n=1,10^7,if(sigma(n+sigma(n))==5*sigma(n),print1(n,", "))) \\ Derek Orr, Sep 07 2014
Showing 1-4 of 4 results.

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