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 1-5 of 5 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

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

A246914 Primes p such that sigma(2p+1) = 3*(p+1).

Original entry on oeis.org

7, 103, 1487, 9679, 73727, 603679
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Comments

Primes p such that sigma(p+sigma(p)) = 3*sigma(p). Subsequence of A246910.
The next term, if it exists, must be greater than 10^9.
Conjecture: Also primes p such that sigma(2p+1) mod p = 3. - Jaroslav Krizek, Sep 28 2014
No other terms up to 10^11. - Michel Marcus, Feb 21 2020

Examples

			Prime 7 is in sequence because sigma(2*7 + 1) = sigma(15) = 24 = 3*(7+1).

Crossrefs

Cf. A000203, A246456, A246910.

Programs

  • Magma
    [n:n in[1..10^7] | SumOfDivisors(n+SumOfDivisors(n))eq 3*SumOfDivisors(n) and IsPrime(n)]
  • Maple
    with(numtheory): A246914:=n->`if`(isprime(n) and sigma(2*n+1) = 3*(n+1), n, NULL): seq(A246914(n), n=1..10^5); # Wesley Ivan Hurt, Oct 01 2014
  • Mathematica
    Select[Prime[Range[1500]], DivisorSigma[1, 2# + 1] == 3# + 3 &] (* Alonso del Arte, Sep 07 2014 *)
  • PARI
    for(n=1,10^6,p=prime(n);if(sigma(p+sigma(p))==3*sigma(p),print1(p,", "))) \\ Derek Orr, Sep 07 2014
  • PARI
    forprime(p=2,10^7,if(sigma(2*p+1)==3*(p+1),print1(p,","))) \\ Edward Jiang, Sep 07 2014

A246911 Numbers n such that sigma(n+sigma(n)) = 4*sigma(n).

Original entry on oeis.org

28, 66, 348, 496, 840, 920, 1320, 1416, 1602, 1770, 1896, 1920, 2040, 2280, 2556, 3000, 3360, 3720, 4440, 4920, 5456, 5640, 5826, 7080, 7392, 8010, 8040, 8128, 8298, 10528, 10680, 11424, 12768, 12840, 13080, 15108, 15504, 17880, 18120, 18720, 18840, 20832
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Examples

			Number 28 (with sigma(28) = 56) is in sequence because sigma(26+sigma(26)) = sigma(84) = 224 = 4*56.

Crossrefs

Cf. A000203, A239050, A246456, A246909, A246910, A246912, A246913, A246914.

Programs

  • Magma
    [n:n in[1..10000] | SumOfDivisors(n+SumOfDivisors(n)) eq 4*SumOfDivisors(n)]
  • Maple
    with(numtheory): A246911:=n->`if`(sigma(n+sigma(n)) = 4*sigma(n),n,NULL): seq(A246911(n), n=1..3*10^4); # Wesley Ivan Hurt, Sep 07 2014
  • PARI
    for(n=1,10^4,if(sigma(n+sigma(n))==4*sigma(n),print1(n,", "))) \\ Derek Orr, Sep 07 2014
Showing 1-5 of 5 results.

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