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.

A231587 Numbers k such that sigma(sigma(k)) - sigma(k) + 1 is prime.

Original entry on oeis.org

2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 19, 23, 24, 25, 29, 34, 37, 38, 42, 43, 48, 53, 54, 56, 57, 59, 60, 62, 63, 64, 67, 69, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 87, 88, 90, 91, 92, 95, 103, 104, 105, 107, 109, 111, 112, 113, 116, 118, 120, 122, 123, 124
Offset: 1

Views

Author

K. D. Bajpai, Nov 11 2013

Keywords

Examples

			a(3) = 5: sigma(sigma(5))-sigma(5)+1 = 12-6+1 = 7, which is prime.
a(10) = 15: sigma(sigma(15))-sigma(15)+1 = 60-24+1 = 37, which is prime.

Links

Crossrefs

Cf. A000203 (a(n): sigma(n)).
Cf. A051027 (a(n): sigma(sigma(n))).
Cf. A228567 (primes: sigma(sigma(n))-sigma(n)).

Programs

  • Maple
    with(numtheory):KD := proc() local a; a:= sigma(sigma(n))-sigma(n)+1; if isprime(a) then RETURN (n); fi; end: seq(KD(),n=1..500);

A231627 Numbers k such that sigma(sigma(k)) - sigma(k) - 1 is prime.

Original entry on oeis.org

3, 5, 20, 24, 26, 29, 38, 41, 44, 45, 54, 56, 59, 60, 65, 78, 80, 81, 83, 87, 90, 92, 95, 101, 102, 108, 110, 114, 120, 122, 123, 135, 136, 137, 142, 143, 146, 147, 150, 153, 158, 159, 164, 167, 168, 174, 176, 177, 178, 180, 184, 185, 187, 190, 194, 197, 203, 209
Offset: 1

Views

Author

K. D. Bajpai, Nov 11 2013

Keywords

Examples

			a(4) = 24: sigma(sigma(n))-sigma(n)-1 = 168-60-1 = 107, which is prime.
a(10) = 45: sigma(sigma(n))-sigma(n)-1 = 168-78-1 = 89, which is prime.

Links

Crossrefs

Cf. A000203 (a(n): sigma(n)).
Cf. A051027 (a(n): sigma(sigma(n))).
Cf. A228567 (primes: sigma(sigma(n))-sigma(n)).
Cf. A231587 (numbers n: sigma(sigma(n))-sigma(n)+1 is prime).

Programs

  • Maple
    with(numtheory): KD := proc() local a; a:= sigma(sigma(n))-sigma(n)-1; if isprime(a) then RETURN (n); fi; end: seq(KD(),n=1..500);
  • Mathematica
    Select[Range[300],PrimeQ[DivisorSigma[1,DivisorSigma[1,#]]-DivisorSigma[ 1,#]-1]&] (* Harvey P. Dale, Jun 04 2021 *)

A233865 Numbers n such that sigma(sigma(n))+1 is prime.

Original entry on oeis.org

1, 2, 5, 6, 11, 14, 15, 19, 20, 23, 26, 29, 36, 37, 41, 61, 63, 67, 68, 72, 74, 76, 82, 85, 86, 88, 90, 100, 102, 103, 104, 105, 107, 110, 113, 116, 117, 118, 120, 128, 129, 131, 133, 139, 141, 142, 144, 145, 146, 149, 153, 155, 157, 159, 161, 172, 174, 179, 181
Offset: 1

Views

Author

K. D. Bajpai, Dec 17 2013

Keywords

Examples

			6 is in the sequence because sigma(sigma(6))+1= 29, which is prime.
19 is in the sequence because sigma(sigma(19))+1= 43, which is prime.

Links

Crossrefs

Cf. A000203 (sigma(n): sum of divisors of n).
Cf. A019279 (superperfect numbers: sigma(sigma(n))).
Cf. A023194 (numbers n: sigma(n)is prime).
Cf. A228567 (primes: sigma(sigma(n))-sigma(n) is prime).

Programs

  • Maple
    with(numtheory): KD := proc() local a; a:= sigma(sigma(n))+1; if isprime(a) then RETURN (n); fi; end: seq(KD(),n=1..500);
  • Mathematica
    Select[Range[200],PrimeQ[DivisorSigma[1,DivisorSigma[1,#]]+1]&] (* Harvey P. Dale, Jan 29 2021 *)
  • PARI
    is(n)=isprime(sigma(sigma(n))+1) \\ Charles R Greathouse IV, Jun 13 2017
Showing 1-3 of 3 results.

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

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