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.

A114519 a(n) = A008475(A114518(n)).

Original entry on oeis.org

2, 3, 5, 5, 7, 7, 11, 7, 13, 17, 11, 19, 13, 23, 11, 11, 29, 31, 19, 13, 37, 13, 41, 43, 47, 19, 17, 53, 29, 31, 59, 61, 67, 71, 17, 73, 23, 79, 43, 83, 19, 89, 97, 29, 101, 103, 107, 31, 109, 23, 113, 61, 127, 131, 137, 139, 73, 41, 149, 151, 157, 37, 83, 163, 19, 167, 47
Offset: 1

Views

Author

Leroy Quet, Dec 05 2005

Keywords

Examples

			A114518(15) = 24 = 2^3 * 3 and 2^3 + 3 = 11 (which is prime). So a(15) = 11.

Links

Crossrefs

Cf. A008475, A114518.

Programs

  • Mathematica
    f[n_] := Plus @@ Power @@@ FactorInteger[n]; Select[f /@ Range[175], PrimeQ[ # ] &] (* Ray Chandler, Dec 07 2005 *)
  • PARI
    A008475(n)=local(t);if(n<1,0,t=factor(n);sum(k=1,matsize(t)[1],t[k,1]^t[k,2])); for(i=1,500,if(isprime(A008475(i)),print1(A008475(i),","))) (Herrgesell)

Extensions

Extended by Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

A114520 Composites in sequence A114518.

Original entry on oeis.org

6, 10, 12, 18, 22, 24, 28, 34, 36, 40, 48, 52, 54, 58, 72, 76, 82, 88, 100, 108, 112, 118, 142, 148, 160, 162, 165, 172, 184, 192, 196, 202, 208, 210, 214, 232, 250, 268, 273, 274, 288, 298, 316, 345, 352, 358, 382, 384, 385, 388, 390, 394, 399, 400, 412, 420
Offset: 1

Views

Author

Leroy Quet, Dec 05 2005

Keywords

Examples

			24 is a composite. 24 = 2^3 * 3 and 2^3 + 3 = 11, which is prime. So 24 is in the sequence.

Crossrefs

Cf. A008475, A114518, A114521, A047820.

Programs

  • Mathematica
    f[n_] := Plus @@ Power @@@ FactorInteger[n]; Select[Select[Range[425], PrimeQ[f[ # ]] &], ! PrimeQ[ # ] &] (* Ray Chandler, Dec 07 2005 *)
  • PARI
    A008475(n)=local(t);if(n<1,0,t=factor(n);sum(k=1,matsize(t)[1],t[k,1]^t[k,2])); for(i=1,700,if(!isprime(i)&&isprime(A008475(i)),print1(i,","))) (Herrgesell)

Extensions

Extended by Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

A114522 Numbers n such that sum of distinct prime divisors of n is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23, 24, 25, 27, 29, 31, 32, 34, 36, 37, 40, 41, 43, 44, 47, 48, 49, 50, 53, 54, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 81, 82, 83, 88, 89, 96, 97, 100, 101, 103, 107, 108, 109, 113, 116, 118, 121, 125, 127
Offset: 1

Views

Author

Leroy Quet, Dec 05 2005

Keywords

Comments

Sequence is the union of the primes and sequence A047820.

Examples

			24 = 2^3 * 3 and 2 + 3 = 5, which is prime. So 24 is included.

Links

Crossrefs

Cf. A000079, A003586, A003592.
Cf. A008472, A047820, A108605, A114518.

Programs

  • Magma
    [k:k in [2..150]| IsPrime(&+PrimeDivisors(k))]; // Marius A. Burtea, Oct 06 2019
  • Mathematica
    f[n_] := Plus @@ First /@ FactorInteger[n]; Select[Range[130], PrimeQ[f[ # ]] &] (* Ray Chandler, Dec 07 2005 *)
Select[Range@127, PrimeQ[Plus @@ First /@ FactorInteger@# ] &] (* Robert G. Wilson v, Dec 07 2005 *)
  • PARI
    for(n=1, 200, v=factor(n); s=0; for(i=1,matsize(v)[1],s+=v[i,1]); if(isprime(s), print1(n, ", "))) \\ Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

Extensions

Extended by Robert G. Wilson v, Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

A114521 a(n) = A008475(A114520(n)).

Original entry on oeis.org

5, 7, 7, 11, 13, 11, 11, 19, 13, 13, 19, 17, 29, 31, 17, 23, 43, 19, 29, 31, 23, 61, 73, 41, 37, 83, 19, 47, 31, 67, 53, 103, 29, 17, 109, 37, 127, 71, 23, 139, 41, 151, 83, 31, 43, 181, 193, 131, 23, 101, 23, 199, 29, 41, 107, 19, 61, 43, 37, 113, 71, 229, 23, 67, 241
Offset: 1

Views

Author

Leroy Quet, Dec 05 2005

Keywords

Examples

			24 (which is composite) is the sixth term of sequence A114520. 24 = 2^3 * 3 and 2^3 + 3 = 11 (which is prime). So a(6) = 11.

Crossrefs

Cf. A008475, A114518, A114519, A114520, A047820.

Programs

  • Mathematica
    f[n_] := Plus @@ Power @@@ FactorInteger[n]; f /@ Select[Select[Range[500], PrimeQ[f[ # ]] &], ! PrimeQ[ # ] &] (* Ray Chandler, Dec 07 2005 *)
  • PARI
    A008475(n)=local(t);if(n<1,0,t=factor(n);sum(k=1,matsize(t)[1],t[k,1]^t[k,2])); for(i=1,900,if(!isprime(i)&&isprime(A008475(i)),print1(A008475(i),","))) (Herrgesell)

Extensions

Extended by Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

A163408 Positive integers n such that A008475(n) is composite.

Original entry on oeis.org

4, 8, 9, 14, 15, 16, 20, 21, 25, 26, 27, 30, 32, 33, 35, 38, 39, 42, 44, 45, 46, 49, 50, 51, 55, 56, 57, 60, 62, 63, 64, 65, 66, 68, 69, 70, 74, 75, 77, 78, 80, 81, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106, 110, 111, 114, 115, 116
Offset: 1

Views

Author

Leroy Quet, Jul 27 2009

Keywords

Comments

Every integer >=2 is exclusively either in this sequence or in sequence A114518.

Crossrefs

A008475, A114518, A163409

Extensions

More terms from Franklin T. Adams-Watters, Aug 25 2011
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.