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.

A076397 Largest prime factor of n-th perfect power.

Original entry on oeis.org

1, 2, 2, 3, 2, 5, 3, 2, 3, 7, 2, 3, 5, 11, 5, 2, 3, 13, 7, 3, 5, 3, 2, 17, 3, 7, 19, 5, 7, 11, 2, 23, 3, 5, 13, 3, 7, 29, 5, 31, 5, 2, 11, 17, 7, 3, 11, 37, 19, 13, 5, 41, 3, 7, 43, 11, 5, 2, 23, 3, 13, 47, 3, 7, 5, 17, 13, 7, 53, 3, 11, 5, 7, 19, 29, 5, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 23
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 09 2002

Keywords

Comments

a(n) = A006530(A001597(n)).

Links

Crossrefs

Cf. A025478, A076396, A076403.

Programs

  • Haskell
    a076397 = a006530 . a025478 -- Reinhard Zumkeller, Mar 28 2014
  • Mathematica
    perfPQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1; Join[ {1},FactorInteger[ #][[-1,1]]&/@ Select[Range[5000],perfPQ]] (* Harvey P. Dale, Sep 12 2021 *)

Formula

a(n) = A006530(A025478(n)).

A122443 Least prime factor of powers of semiprimes.

Original entry on oeis.org

1, 2, 2, 3, 2, 2, 3, 2, 3, 2, 5, 2, 3, 2, 5, 2, 2, 3, 2, 7, 3, 5, 3, 2, 2, 2, 5, 3, 2, 7, 3, 2, 5, 2, 3, 7, 3, 2, 5, 2, 2, 3, 5, 2, 7, 11, 2, 3, 3, 7, 2, 3, 2, 11, 5, 2, 5, 2, 3, 7, 2, 13, 3, 2, 3, 5, 11, 2, 2, 3, 2, 7, 5, 2, 11, 3, 2, 5, 2, 7, 2, 3, 13, 3, 2, 5, 3, 13
Offset: 1

Views

Author

Jonathan Vos Post, Sep 06 2006

Keywords

Links

Crossrefs

Cf. A000040, A001358, A020639, A076396, A085155.
Cf. A122444 (greatest prime factor of powers of semiprimes).
Cf. A076396 (smallest prime factor of n-th perfect power).

Programs

  • Mathematica
    FactorInteger[#][[1, 1]] & /@ Select[Range@ 250, Function[n, Or[n == 1, And[Length@ # == 1, EvenQ@ First@ #], And[Length@ # == 2, SameQ @@ #]] &[FactorInteger[n][[All, -1]]]]] (* Michael De Vlieger, Mar 04 2017 *)
  • PARI
    is(n)=my(f=factor(n)[, 2]); #f==0 || (#f==2 && f[1]==f[2]) || (#f==1 && f[1]%2==0);
spf(n) = if (n==1, 1, factor(n)[1,1]);
lista(nn) = {for (n=1, nn, if (is(n), print1(spf(n), ", ")););} \\ Michel Marcus, Mar 04 2017

Formula

a(n) = A020639(A085155(n)) = least prime factor of A085155 powers of semiprimes.

Extensions

More terms from Michel Marcus, Mar 04 2017

A122444 Greatest prime factor of powers of semiprimes.

Original entry on oeis.org

1, 2, 3, 3, 5, 7, 5, 2, 7, 11, 5, 13, 11, 17, 7, 3, 19, 13, 23, 7, 17, 11, 19, 29, 31, 2, 13, 23, 37, 11, 3, 41, 17, 43, 29, 13, 31, 47, 19, 5, 53, 37, 23, 59, 17, 11, 61, 41, 43, 19, 67, 47, 71, 13, 29, 73, 31, 79, 53, 23, 83
Offset: 1

Views

Author

Jonathan Vos Post, Sep 06 2006

Keywords

Comments

A122443 is least prime factor of powers of semiprimes. Cf. A076397 Largest prime factor of n-th perfect power.

Links

Crossrefs

Cf. A000040, A001358, A006530, A020639, A076396, A076397, A085155, A122443.

Programs

  • Mathematica
    FactorInteger[#][[-1, 1]] & /@ Select[Range@ 168, Function[n, Or[n == 1, And[Length@ # == 1, EvenQ@ First@ #], And[Length@ # == 2, SameQ @@ #]] &[FactorInteger[n][[All, -1]]]]] (* Michael De Vlieger, Mar 04 2017 *)

Formula

a(n) = A006530(A085155(n)) = greatest prime factor of A085155 powers of semiprimes.
Showing 1-3 of 3 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.