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.

A116035 Numbers k such that k + phi(k) + sigma(k) is a prime.

Original entry on oeis.org

1, 4, 15, 33, 35, 36, 50, 55, 57, 64, 65, 75, 77, 85, 87, 93, 98, 115, 119, 129, 133, 143, 155, 159, 185, 187, 189, 205, 213, 215, 217, 219, 242, 243, 247, 253, 265, 287, 295, 303, 309, 323, 324, 327, 339, 345, 365, 385, 393, 395, 407, 425, 427, 453, 469, 493
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			205 + phi(205) + sigma(205) = 617 (prime).

Links

Crossrefs

Cf. A078762, A068080.

Programs

  • Mathematica
    Select[Range[500],PrimeQ[#+EulerPhi[#]+DivisorSigma[1,#]]&] (* Harvey P. Dale, Nov 09 2014 *)

A116050 n+sigma(n)+sigma(sigma(n)) is a prime.

Original entry on oeis.org

1, 4, 5, 8, 10, 16, 18, 22, 23, 27, 29, 32, 36, 41, 46, 50, 53, 65, 66, 70, 94, 99, 101, 106, 111, 113, 125, 129, 131, 137, 171, 183, 195, 197, 200, 201, 203, 209, 210, 221, 233, 237, 239, 245, 251, 269, 275, 299, 301, 309, 317, 321, 322, 327, 329, 333, 335
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			8 + sigma(8) + sigma(sigma(8)) = 47.

Links

Crossrefs

Cf. A078762.

Programs

  • Mathematica
    dsQ[n_]:=Module[{dsn=DivisorSigma[1,n]},PrimeQ[n+dsn+DivisorSigma[1,dsn]]]; Select[Range[400],dsQ] (* Harvey P. Dale, May 15 2013 *)

A158458 Numbers k such that k + bigomega(k) is prime.

Original entry on oeis.org

2, 8, 9, 15, 20, 21, 28, 32, 35, 39, 44, 48, 50, 51, 57, 65, 68, 69, 70, 76, 77, 87, 95, 98, 108, 110, 111, 124, 129, 135, 148, 154, 155, 161, 162, 164, 168, 170, 176, 177, 188, 189, 190, 192, 209, 221, 225, 230, 236, 237, 238, 249, 252, 264, 266, 267, 268, 272, 290
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 19 2009

Keywords

Comments

2 is the only prime number in the sequence. - Michel Lagneau, May 17 2010

Examples

			a(2) = 8 = 2*2*2; 8+3 = 11 is prime.
a(3) = 9 = 3*3; 9+2 = 11 is prime.
a(4) = 15 = 3*5; 15+2 = 17 is prime.

Links

Crossrefs

Cf. A000040, A001222.
Cf. A067532, A078762, A068080. - Michel Lagneau, May 17 2010

Programs

  • Maple
    for k from 2 to 400 do if isprime(k+numtheory[bigomega](k)) then printf("%d,",k) ; fi; od: # R. J. Mathar, May 19 2009, May 23 2010
  • Mathematica
    Select[Range[10^3], PrimeQ[ # + Plus @@ Last /@ FactorInteger[ # ]] &] (* Michel Lagneau, May 17 2010 *)
Select[Range[300],PrimeQ[#+PrimeOmega[#]]&] (* Harvey P. Dale, Dec 20 2021 *)
  • PARI
    is(n)=isprime(n+bigomega(n)) \\ Eric Chen, Jun 13 2018

Formula

{k: k+A001222(k) in A000040}.

Extensions

191 replaced with 192 and extended by R. J. Mathar, May 19 2009
Generalized (by inserting a(1)=2) by Michel Lagneau, May 17 2010

A246908 a(n) = sigma(n + sigma(n)) - sigma(n).

Original entry on oeis.org

2, 3, 4, 5, 6, 27, 16, 9, 23, 38, 12, 62, 26, 36, 32, 17, 30, 41, 36, 54, 22, 54, 24, 164, 89, 84, 28, 168, 30, 144, 72, 57, 73, 126, 36, 37, 86, 111, 64, 162, 42, 192, 76, 171, 90, 108, 72, 184, 105, 75, 96, 274, 54, 240, 56, 252, 58, 176, 84, 392, 106, 144
Offset: 1

Views

Author

Jaroslav Krizek, Sep 07 2014

Keywords

Examples

			For n = 6; a(n) = sigma(6 + sigma(6)) - sigma(6) = sigma(18) - sigma(6) = 39 - 12 = 27.

Links

Crossrefs

Cf. A000203, A078762, A246456.

Programs

  • Magma
    [SumOfDivisors(n+SumOfDivisors(n))-SumOfDivisors(n):n in[1..1000]]
  • Mathematica
    sig[n_]:=Module[{d6=DivisorSigma[1,n]},DivisorSigma[1,n+d6]-d6]; Array[ sig,70] (* Harvey P. Dale, Feb 20 2015 *)
  • PARI
    vector(100,n,sigma(n+sigma(n))-sigma(n)) \\ Derek Orr, Sep 07 2014

Formula

a(n) = n + 1 for number in A078762 (numbers n such that n + sigma(n) is prime).

A249486 Nonprime numbers n such that sigma(n) + n is prime.

Original entry on oeis.org

1, 4, 8, 16, 21, 27, 35, 36, 55, 57, 63, 64, 65, 75, 77, 85, 98, 100, 111, 119, 125, 128, 133, 143, 144, 155, 161, 171, 183, 189, 203, 205, 209, 215, 235, 237, 242, 243, 245, 253, 259, 275, 291, 301, 305, 323, 324, 333, 335, 338, 343, 351, 355, 365, 377, 391
Offset: 1

Views

Author

Jaroslav Krizek, Nov 13 2014

Keywords

Comments

Complement of A005384 (Sophie Germain primes) with respect to A078762 (numbers n such that n + sigma(n) is prime).

Examples

			Number 8 is in sequence because sigma(8)+8 = 15+8 = 23 (prime).

Crossrefs

Cf. A000040, A000203, A018252, A005384, A078762.

Programs

  • Magma
    [n: n in[1..10000] | IsPrime(SumOfDivisors(n)+ n) and not IsPrime(n) ]
  • Maple
    select(n -> not isprime(n) and isprime(n + numtheory:-sigma(n)), [$1..1000]); # Robert Israel, Nov 13 2014
  • Mathematica
    Select[Range[500], PrimeQ[DivisorSigma[1, #] + #]&& !PrimeQ[#] &] (* Vincenzo Librandi, Nov 14 2014 *)
  • PARI
    print1(1,", ");forcomposite(n=1,1000,if(isprime(sigma(n)+n),print1(n,", "))) \\ Derek Orr, Nov 13 2014
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.