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.

A231546 Numbers k such that sigma(k) = sigma(k-1).

Original entry on oeis.org

15, 207, 958, 1335, 1365, 1635, 2686, 2975, 4365, 14842, 18874, 19359, 20146, 24958, 33999, 36567, 42819, 56565, 64666, 74919, 79827, 79834, 84135, 92686, 109215, 111507, 116938, 122074, 138238, 147455, 161002, 162603, 166935, 174718, 190774, 193894, 201598
Offset: 1

Views

Author

Jaroslav Krizek, Nov 11 2013

Keywords

Comments

Also, numbers k such that k = antisigma(k) - antisigma(k-1), where antisigma(k) = A024816(k) = the sum of the non-divisors of k that are between 1 and k.

Examples

			15 = antisigma(15) - antisigma(14) = 96 - 81.

Links

Crossrefs

Cf. A002961, A024816 (antisigma(n)), A231545 (numbers n such that antisigma(n) = antisigma(n-1)).

Programs

  • Mathematica
    SequencePosition[DivisorSigma[1,Range[210000]],{x_,x_}][[;;,2]] (* Harvey P. Dale, May 28 2024 *)
  • PARI
    n=0;sp=sigma(2);for(k=3,oo,my(s=sigma(k));if(s==sp,print1(k,", ");n++;if(n>36,break));sp=s) \\ Hugo Pfoertner, Mar 06 2020

Formula

a(n) = A002961(n) + 1.

Extensions

More terms from Hugo Pfoertner, Mar 06 2020

A231547 Numbers n such that n < sigma(n) - sigma(n-1).

Original entry on oeis.org

12, 18, 20, 24, 30, 36, 42, 48, 54, 60, 72, 80, 84, 90, 96, 102, 104, 108, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 180, 192, 198, 200, 204, 210, 216, 224, 228, 234, 240, 252, 258, 260, 264, 270, 272, 276, 280, 282, 288, 294, 300, 306
Offset: 1

Views

Author

Jaroslav Krizek, Nov 12 2013

Keywords

Comments

Also numbers n such that antisigma(n) < antisigma(n-1), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.
Numbers n such that A163553(n-1) < 0.
Numbers n such that antisigma(n) > antisigma(n-1) = A231711.
Numbers n such that antisigma(n) = antisigma(n-1) = A231545.
Complement of union of A231711, A231545 and number 1.
Does this sequence have a density? - Charles R Greathouse IV, Jul 14 2024

Examples

			12 is in sequence because antisigma(12) = 50 < antisigma(11) = 54.

Links

Crossrefs

Cf. A231545, A231546, A231711, A231548, A024816, A163553.

Programs

  • Mathematica
    Select[Range[350],#<(DivisorSigma[1,#]-DivisorSigma[1,#-1])&] (* Harvey P. Dale, May 26 2016 *)
  • PARI
    is(n)=nCharles R Greathouse IV, Jul 14 2024

A231711 Numbers n such that n > sigma(n) - sigma(n-1).

Original entry on oeis.org

3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82
Offset: 1

Views

Author

Jaroslav Krizek, Nov 12 2013

Keywords

Comments

Numbers n such that antisigma(n) > antisigma(n-1), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.
Numbers n such that A163553(n-1) > 0.
Numbers n such that antisigma(n) < antisigma(n-1) = A231547.
Numbers n such that antisigma(n) = antisigma(n-1) = A231545.
Complement of union of A231547, A231545 and number 1.

Examples

			10 is in sequence because antisigma(10) = 37 > antisigma(9) = 32.

Links

Crossrefs

Cf. A231545, A231546, A231547, A231548, A024816, A163553.

Programs

  • Maple
    with(numtheory); A231711:=n->`if`(sigma(n)-sigma(n-1)A231711(n), n=1..100); # Wesley Ivan Hurt, Nov 14 2013
  • PARI
    isok(n) = n > sigma(n) - sigma(n-1); \\ Michel Marcus, Nov 14 2013
Showing 1-3 of 3 results.

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

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